# Math Help - solve for x: with log bases

1. ## solve for x: with log bases

solve for x: log7(x+8) - log7(x-1) = log710

2. Originally Posted by robinpatrick
solve for x: log7(x+8) - log7(x-1) = log710
Okay, use the fact,
$\log(a/b)=\log(a)-\log(b)$
Thus,
$\log_7 (x+8)-\log_7(x-1)=\log_7 10$
Becomes,
$\log_7 \left( \frac{x+8}{x-1} \right)=\log_7 10$
This logarithm function is one-to-one,
$\frac{x+8}{x-1}=\frac{10}{1}$
Thus, cross multiply
$x+8=10(x-1)$
Thus,
$x+8=10x-10$
Thus,
$9x=18$
Thus,
$x=2$
Check solution and see that it works