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with something called logarithms.

So 1 = (1 + x)^5

log 1 = log ((1+x)^5)

log 1 = 5 x log (1 +x)

but log 1 = 0

therefore 0 = 5 x log(1+x)

divide both sides by 5 and you get 0 = log (1+x)

we know that log 1 = 0, therefore 1+ x = 1 and so x = 0

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