SOLUTION: solve the logarithmic expression be sure to reject any values of x that are not in the domain of the original logarithmic expressions. give exact answer. [log(base5)(x-7)] + [log(

Question 681936: solve the logarithmic expression be sure to reject any values of x that are not in the domain of the original logarithmic expressions. give exact answer.
[log(base5)(x-7)] + [log(base5)(x+17)]=2
i have tried multiple different ways to solve many random generated problems that look like this. (im using mymathlab) this is one of the ones i got wrong. i came to an answer of 3/2 on this one. mymathlab is saying the correct answer is 8, and i dont know how to get to the correct answer of 8. i need to know how to solve a problem like this. if you could help by giving me step-by-step instructions using this example that would be great.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
solve the logarithmic expression be sure to reject any values of x that are not in the domain of the original logarithmic expressions. give exact answer.
[log(base5)(x-7)] + [log(base5)(x+17)]=2
**
log5(x-7)+log5(x+17)=2
log5(x-7)(x+17)=log5(25)
log5(25)=2
(x-7)(x+17)=25
x^2+10x-119=25
x^2+10x-144=0
(x-8)(x+18)=0
x=-18 (reject,(x+17)>0)
x=8
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