Answer
$x=\dfrac{9}{2}=4.5$
Work Step by Step
Apply the logarithmic property:
$\log_a(\dfrac{M}{N}) = \log_a M-\log_a N$
and rearrange the given expression to obtain:
$\log_{a}[\dfrac{x-1}{x+6}] =\log_{a}[\dfrac{x-2}{x+3}]$
This gives: $\dfrac{x-1}{x+6}=\dfrac{x-2}{x+3}$
After cross-multiplying the above, we get the following quadratic equation:
$x^2+2x-3 =x^2+4x -12$
$2x -9 =0 \implies x =4.5$
Thus, our answer is: $x=\dfrac{9}{2}=4.5$
