How do you simplify variables which are powers?

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I have just started learning logarithms and I am struggling to solve the following

$$ \begin{equation} 2^a3^b = 6 \\ 3^a4^b = 6 \end{equation} $$

How can we solve for a and b in this case?

EDIT 1: Cleared up the two equations to increase understanding. Thanks for the heads-up!

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Hint : Taking the natural logarithm on both sides , you get the linear equation system $$\ln(2)\cdot a+\ln(3)\cdot b=\ln(6)$$ $$\ln(3)\cdot a+\ln(4)\cdot b=\ln(6)$$ which should be easy to be solved.