SOLUTION: 2log( x ) = log(2) + log(5x-8) {{{log( x )^2 = log(2) + log(5x-8)}}} {{{log( x )^2 = log(2)(5x-8)}}} you can write {{{( x )^2 = (2)(5x-8)}}} {{{( x )^2 = 10x-16}}} {{{( x )

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 2log( x ) = log(2) + log(5x-8) {{{log( x )^2 = log(2) + log(5x-8)}}} {{{log( x )^2 = log(2)(5x-8)}}} you can write {{{( x )^2 = (2)(5x-8)}}} {{{( x )^2 = 10x-16}}} {{{( x )      Log On


   

Question 104232: 2log( x ) = log(2) + log(5x-8)
log%28+x+%29%5E2+=+log%282%29+%2B+log%285x-8%29
log%28+x+%29%5E2+=+log%282%29%285x-8%29
you can write
%28+x+%29%5E2+=+%282%29%285x-8%29
%28+x+%29%5E2+=+10x-16
%28+x+%29%5E2-10x%2B16=0
x1=%2810-sqrt%28100-64%29%29%2F%282%29
= %2810-6%29%2F2
=2
x2=%2810%2Bsqrt%28100-64%29%29%2F%282%29
= %2810%2B6%29%2F2
=8
SO THERE ARE TWO SOLUTION
8 AND 2
Found 2 solutions by scott8148, bimanewton:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
using rules for logarithms; x^2=2(5x-8)

x^2=10x-16 ... x^2-10x+16=0 ... (x-8)(x-2)=0

Answer by bimanewton(8) About Me  (Show Source):
You can put this solution on YOUR website!
log%28+x+%29%5E2+=+log%282%29+%2B+log%285x-8%29
log%28+x+%29%5E2+=+log%282%29%285x-8%29
you can write
%28+x+%29%5E2+=+%282%29%285x-8%29
%28+x+%29%5E2+=+10x-16
%28+x+%29%5E2-10x%2B16=0
x1=%2810-sqrt%28100-64%29%29%2F%282%29
= %2810-6%29%2F2
=2
x2=%2810%2Bsqrt%28100-64%29%29%2F%282%29
= %2810%2B6%29%2F2
=8
SO THERE ARE TWO SOLUTION
8 AND 2