\sqrt[5]{32^x -1 } } -1 = 0 This Please i don't know how to proceed

Question

`\sqrt[5]{32^x -1 } } -1` = 0 This Please i don't know how to proceed

Answer 1

add 1 to both sides

`\sqrt[5]{32^x-1}=1`
raise each side to the 5th power

`32^x-1=1`
add 1 to both sides

`32^x=2`
we can try to match bases
because if, xᵃ=xᵇ where x=x, then a=b
we know that 32=2⁵
and
`(x^m)^n=x^(mn)` so

`32^x=2` is the same as

`(2^5)^x=2` or
`2^(5x)=2^1`
therefor
5x=1
divide both sides by 5
x=1/5