SOLUTION: Solve: log base2 (x^2-203)=5 (log base 2 x squared minus 203 equals 5)

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Question 170476: Solve: log base2 (x^2-203)=5
(log base 2 x squared minus 203 equals 5)
Found 2 solutions by grnkbul, stanbon:
Answer by grnkbul(2)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/4 = 2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/2 = 4.
  • Slope is -4/2 = -2.
  • Equation in slope-intercept form: y=-2*x+4.
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=2.
  • Graphical form: Equation was fully solved.
  • Text form: x+x-x+2x=6 simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( x+x-x+2x=6 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+x+%29,highlight_red%28+-x+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%281%2B1-1%2B2%29%2Ax+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-6+%29
It becomes .
Look at .
Solved linear equation highlight_red%28+3%2Ax-6=0+%29 equivalent to 3*x-6 =0
It becomes .
Result:
This is an equation! Solutions: x=2.

Universal Simplifier and Solver


Done!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=16 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 3, -1. Here's your graph:
Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values
Your Result:


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: x^2-2x simplifies to 3
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( x^2-2x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Replaced x with 3
It becomes .
Look at .
Replace constants in factor: highlight_red%28+3+%29,highlight_red%28+2+%29 with highlight_green%28+9+%29
It becomes .
Look at .
Replaced x with 3
It becomes .
Look at .
Replace constants in expression: highlight_red%28+9+%29,highlight_red%28+-2%2A3+%29 with highlight_green%28+3+%29
It becomes .
Result:

Universal Simplifier and Solver


Done!
Solved by pluggable solver: SOLVE a linear equation
Solve . Move 1 to the right: . Divide by 2:
Solved by pluggable solver: Linear System solver (using determinant)
Solve:


Any system of equations:


has solution

or



(x=1, y=1}
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/4 = 2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/2 = 4.
  • Slope is -4/2 = -2.
  • Equation in slope-intercept form: y=-2*x+4.
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/4 = 2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/2 = 4.
  • Slope is -4/2 = -2.
  • Equation in slope-intercept form: y=-2*x+4.
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/4 = 2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/2 = 4.
  • Slope is -4/2 = -2.
  • Equation in slope-intercept form: y=-2*x+4.
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/4 = 2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/2 = 4.
  • Slope is -4/2 = -2.
  • Equation in slope-intercept form: y=-2*x+4.
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/4 = 2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/2 = 4.
  • Slope is -4/2 = -2.
  • Equation in slope-intercept form: y=-2*x+4.
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/4 = 2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/2 = 4.
  • Slope is -4/2 = -2.
  • Equation in slope-intercept form: y=-2*x+4.
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=2.
  • Graphical form: Equation was fully solved.
  • Text form: x+x-x+2x=6 simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( x+x-x+2x=6 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+x+%29,highlight_red%28+-x+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%281%2B1-1%2B2%29%2Ax+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-6+%29
It becomes .
Look at .
Solved linear equation highlight_red%28+3%2Ax-6=0+%29 equivalent to 3*x-6 =0
It becomes .
Result:
This is an equation! Solutions: x=2.

Universal Simplifier and Solver


Done!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=2.
  • Graphical form: Equation was fully solved.
  • Text form: x+x-x+2x=6 simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( x+x-x+2x=6 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+x+%29,highlight_red%28+-x+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%281%2B1-1%2B2%29%2Ax+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-6+%29
It becomes .
Look at .
Solved linear equation highlight_red%28+3%2Ax-6=0+%29 equivalent to 3*x-6 =0
It becomes .
Result:
This is an equation! Solutions: x=2.

Universal Simplifier and Solver


Done!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=2.
  • Graphical form: Equation was fully solved.
  • Text form: x+x-x+2x=6 simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( x+x-x+2x=6 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+x+%29,highlight_red%28+-x+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%281%2B1-1%2B2%29%2Ax+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-6+%29
It becomes .
Look at .
Solved linear equation highlight_red%28+3%2Ax-6=0+%29 equivalent to 3*x-6 =0
It becomes .
Result:
This is an equation! Solutions: x=2.

Universal Simplifier and Solver


Done!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=2.
  • Graphical form: Equation was fully solved.
  • Text form: x+x-x+2x=6 simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( x+x-x+2x=6 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+x+%29,highlight_red%28+-x+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%281%2B1-1%2B2%29%2Ax+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-6+%29
It becomes .
Look at .
Solved linear equation highlight_red%28+3%2Ax-6=0+%29 equivalent to 3*x-6 =0
It becomes .
Result:
This is an equation! Solutions: x=2.

Universal Simplifier and Solver


Done!
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
log base2 (x^2-203)=5
x^2-203 = 2^5
x^2 - 203 = 32
x^2 = 235
x= +/- sqrt(235) = +/-15.32971
Positive solution:
x = 15.32971
===================
Cheers,
Stan H.
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