Question

solve for x: log6(x+29) - log6(x-6) = 2

Answer 1

$log_6(x+29)-log_6(x-6)=2$
$log_6{6^2}=2$
$log_6(x+29)-log_6(x-6)=log_6{6^2}=log_6{36}$
$log_6(x+29)-log_6(x-6)=\frac{log_6(x+29)}{log_6(x-6)}=log_6{36}$
$\frac{x+29}{x-6}=36$
$x+29=36(x-6)$
$x+29=36x-216$
$35x=245$
$x=\frac{245}{35}=7$
$log_6{36}-log_6{1}=2$