$4^{3a-1}-5^{2b-3}=0$ find a in terms of $b$

Question

If $4^{3a-1}-5^{2b-3}=0$ then find a using $b$.

My Attempt:we know that $2^{6a-2}=5^{2b-3}$ with this way we can find a value for $a$ and $b$ if both sides are zero if we can find another value for $a$ and $b$ the question will solved.

Answer 1

HINT:

$$2^{2(3a-1)}=5^{2b-3}$$

Take logarithm to find $$2(3a-1)\log2=(2b-3)\log5$$