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

1 Answer

5 votes
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
User Yulisa
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