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

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- Oct 23rd 2006, 07:19 PMrobinpatricksolve for x: with log bases
solve for x: log7(x+8) - log7(x-1) = log710

- Oct 23rd 2006, 07:28 PMThePerfectHacker
Okay, use the fact,

$\displaystyle \log(a/b)=\log(a)-\log(b)$

Thus,

$\displaystyle \log_7 (x+8)-\log_7(x-1)=\log_7 10$

Becomes,

$\displaystyle \log_7 \left( \frac{x+8}{x-1} \right)=\log_7 10$

This logarithm function is one-to-one,

$\displaystyle \frac{x+8}{x-1}=\frac{10}{1}$

Thus, cross multiply

$\displaystyle x+8=10(x-1)$

Thus,

$\displaystyle x+8=10x-10$

Thus,

$\displaystyle 9x=18$

Thus,

$\displaystyle x=2$

Check solution and see that it works