SOLUTION: ln(4x + 4) + ln(6x - 6) = 0 has a positive solution for x. Enter the solution

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Question 308982: ln(4x + 4) + ln(6x - 6) = 0 has a positive solution for x. Enter the solution
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
it is actually very easy.
ln%284x+%2B+4%29+%2B+ln%286x+-+6%29+=+0
ln%28%284x+%2B+4%29%2A%286x+-+6%29%29+=+0
%284x+%2B+4%29%2A%286x+-+6%29+=+1
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=1.02062072615966,x=-1.02062072615966.
  • Graphical form: Equation %284x%2B4%29%2A%286x-6%29=1 was fully solved.
  • Text form: (4x+4)*(6x-6)=1 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%284x%2B4%29%2A%286x-6%29=1+%29
    For tutors: simplify_cartoon( (4x+4)*(6x-6)=1 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at %284%2Ax%2B4%29%2A%286%2Ax-6%29=highlight_red%28+1+%29.
Moved these terms to the left highlight_green%28+-1+%29
It becomes %284%2Ax%2B4%29%2A%286%2Ax-6%29-highlight_green%28+1+%29=0.
Look at highlight_red%28+%284%2Ax%2B4%29%2A%286%2Ax-6%29+%29-1=0.
Expanded term %286%2Ax-6%29 by using associative property on %284%2Ax%2B4%29
It becomes highlight_green%28+%286%2Ax-6%29%2A4%2Ax+%29%2Bhighlight_green%28+%286%2Ax-6%29%2A4+%29-1=0.
Look at highlight_red%28+%286%2Ax-6%29%2A4%2Ax+%29%2B%286%2Ax-6%29%2A4-1=0.
Expanded term 4%2Ax by using associative property on %286%2Ax-6%29
It becomes .
Look at highlight_red%28+4+%29%2Ax%2Ahighlight_red%28+6+%29%2Ax-4%2Ax%2A6%2B%286%2Ax-6%29%2A4-1=0.
Multiplied numerator integers
It becomes highlight_green%28+24+%29%2Ax%2Ax-4%2Ax%2A6%2B%286%2Ax-6%29%2A4-1=0.
Look at 24%2Ax%2Ax-highlight_red%28+4+%29%2Ax%2Ahighlight_red%28+6+%29%2B%286%2Ax-6%29%2A4-1=0.
Multiplied numerator integers
It becomes 24%2Ax%2Ax-highlight_green%28+24+%29%2Ax%2B%286%2Ax-6%29%2A4-1=0.
Look at 24%2Ahighlight_red%28+x+%29%2Ahighlight_red%28+x+%29-24%2Ax%2B%286%2Ax-6%29%2A4-1=0.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E2+%29
It becomes 24%2Ahighlight_green%28+x%5E2+%29-24%2Ax%2B%286%2Ax-6%29%2A4-1=0.
Look at 24%2Ax%5E2-24%2Ax%2Bhighlight_red%28+%286%2Ax-6%29%2A4+%29-1=0.
Expanded term 4 by using associative property on %286%2Ax-6%29
It becomes 24%2Ax%5E2-24%2Ax%2Bhighlight_green%28+4%2A6%2Ax+%29-highlight_green%28+4%2A6+%29-1=0.
Look at 24%2Ax%5E2-24%2Ax%2Bhighlight_red%28+4+%29%2Ahighlight_red%28+6+%29%2Ax-4%2A6-1=0.
Multiplied numerator integers
It becomes 24%2Ax%5E2-24%2Ax%2Bhighlight_green%28+24+%29%2Ax-4%2A6-1=0.
Look at 24%2Ax%5E2-24%2Ax%2B24%2Ax-highlight_red%28+4+%29%2Ahighlight_red%28+6+%29-1=0.
Multiplied numerator integers
It becomes 24%2Ax%5E2-24%2Ax%2B24%2Ax-highlight_green%28+24+%29-1=0.
Look at 24%2Ax%5E2-24%2Ax%2B24%2Ax-highlight_red%28+24+%29-highlight_red%28+1+%29=0.
Added fractions or integers together
It becomes 24%2Ax%5E2-24%2Ax%2B24%2Ax%2Bhighlight_green%28+-25+%29=0.
Look at 24%2Ax%5E2-24%2Ax%2B24%2Ax%2Bhighlight_red%28+-25+%29=0.
Removed extra sign in front of -25
It becomes 24%2Ax%5E2-24%2Ax%2B24%2Ax-highlight_green%28+25+%29=0.
Look at 24%2Ax%5E2-highlight_red%28+24%2Ax+%29%2Bhighlight_red%28+24%2Ax+%29-25=0.
Eliminated similar terms highlight_red%28+-24%2Ax+%29,highlight_red%28+24%2Ax+%29 replacing them with highlight_green%28+%28-24%2B24%29%2Ax+%29
It becomes 24%2Ax%5E2%2Bhighlight_green%28+%28-24%2B24%29%2Ax+%29-25=0.
Look at 24%2Ax%5E2%2Bhighlight_red%28+%28-24%2B24%29%2Ax+%29-25=0.
Since highlight_red%28+%28-24%2B24%29%2Ax+%29 has zero as a factor, it should be replaced with a zero
Look at 24%2Ax%5E2%2B0-25=0.
Added fractions or integers together
It becomes 24%2Ax%5E2%2B0-25=0.
Look at 24%2Ax%5E2%2Bhighlight_red%28+0+%29-25=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes 24%2Ax%5E2-25=0.
Look at highlight_red%28+24%2Ax%5E2-25+%29=0.
Equation highlight_red%28+24%2Ax%5E2-25=0+%29 is a quadratic equation: 24*x^2-25 =0, and has solutions 1.02062072615966,-1.02062072615966
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=1.02062072615966,x=-1.02062072615966.

Universal Simplifier and Solver


Done!