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=\frac18\cdot8^x\implies\left(\frac38\right)^x=\frac1{72}`

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

`\log_(3/8)\left(\frac38\right)^x=\log_(3/8)\frac1{72}`

`\implies x\log_(3/8)\frac38=-\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.