Logarithm / exponential equation, not sure what to make of this, (simple) Solve for $a:(2 \log_a x)(3 \log_{x^2} 4) = 3$
No idea how to approach this problem other than moving the 2 and the 3 into an exponent..

Use change of base:$\log_xy=\dfrac{\log_ny}{\log_nx}$:
$$(2\log_ax)(3\log_{x^2}4)=(\log_ax^2)(\log_{x^2}4^3)=\frac{\color{red}{\ln x^2}}{\ln a}\cdot\frac{\ln 4^3}{\color{red}{\ln x^2}}=\frac{\ln 4^3}{\ln a}=\log_a4^3=3 \implies a^3=4^3 \implies a=4$$
