Question

3^x+2=8^x-1 Solve for x.

Answer 1

I assume the equation is supposed to be

$3^{x+2}=8^{x-1}$

Then we can write

$9\cdot3^x=\dfrac18\cdot8^x\implies\left(\dfrac38\right)^x=\dfrac1{72}$

Take the logarithm of base 3/8 on both sides:

$\log_{3/8}\left(\dfrac38\right)^x=\log_{3/8}\dfrac1{72}$

$\implies x\log_{3/8}\dfrac38=-\log_{3/8}72$

$\implies x=-\log_{3/8}72$

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If the equation is actually $3^x+2=8^x-1$, I'm afraid it cannot be solved exactly.