What is the value of x? A^3a^x = a^12

Using log(m*n) = log(m) + log(n)  and log(m^n) = n*log(m) we get:

3log(A) + x*log(a) = 12log(a)

x*log(a) = 12log(a) - 3log(A)

x = 12 - 3log(A)/log(a) 

(If A and a are meant to be the same then this reduces to x = 9)

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What is the value of x? A^3a^x = a^12

$$\small{\text{$
\begin{array}{rcl}
A^3a^x &=& a^{12} \\
a^x &=& \dfrac{a^{12}}{A^3} \qquad | \qquad b=\dfrac{a^{12}}{A^3} \\\\
a^x &=& b \qquad | \qquad \ln{()} \\
x\ln{(a)} &=& \ln{(b)}\\\\
\mathbf{x} &\mathbf{=}& \mathbf{\dfrac{ \ln{(b)} }{\ln{(a)} } }\quad $
and $ \mathbf{ \quad b=\dfrac{a^{12}}{A^3} }\\\\
\end{array}
$}}}$$