SOLUTION: Find the largest value of x that satisfies:
log(base5) (x^2) − log(base5) (x+2) = 2
x =
THANKS A LOT!
Algebra.Com
Question 139457: Find the largest value of x that satisfies:
log(base5) (x^2) − log(base5) (x+2) = 2
x =
THANKS A LOT!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation
Combine the logs
Use the relationship <===> to rewrite the equation
Square 5
Multiply both sides by
Distribute
Get all terms to one side
Let's use the quadratic formula to solve for x:
Starting with the general quadratic
the general solution using the quadratic equation is:
So lets solve ( notice , , and )
Plug in a=1, b=-25, and c=-50
Negate -25 to get 25
Square -25 to get 625 (note: remember when you square -25, you must square the negative as well. This is because .)
Multiply to get
Combine like terms in the radicand (everything under the square root)
Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
Multiply 2 and 1 to get 2
So now the expression breaks down into two parts
or
So these expressions approximate to
or
So we can clearly see that is the largest value of x that satisfies the equation
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