How do you solve $log_7(x-3)-log_7x=3$ ?

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Answer 1 · 2016-12-01T05:58:26

$x=-1/114$

Condense the logs on the left -- Subtracting logs of the same base can be rewritten as dividing within the log:
$log_ab-log_ac=log_a(b/c)$

$log_7(x-3)-log_7x=3$
$log_7((x-3)/x)=3$

Now use the log rule: If $log_ab=n$ , then $a^n=b$ .
$7^3=(x-3)/x$

$343=(x-3)/x$

Multiply each side by x:
$343x=x-3$

Subtract x from each side:
$342x=-3$

$x=-3/342$

$x=-1/114$

How do you solve log_7(x-3)-log_7x=3log_7(x-3)-log_7x=3?