What is the answer to y^{y^5}=100 ?

The answer to y^{y^5}=100 is y=\sqrt[5]{10}

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y^{y^5}=100

y^{y^{5}} = 100

Decimal Notation

y = 1.58489 \dots

Solution steps

y^{y^{5}} = 100

Prepare

y^{y^{5}} = 100

for Lambert form:

y e^{- \frac{2 l n ( 10 )}{y ^{5}}} = 1

Rewrite the equation with

\frac{2 ln ( 10 )}{y ^{5}} = u

and

Solve

u = \frac{ln ( 10 )}{5}

Substitute back

u = \frac{2 ln ( 10 )}{y ^{5}},

solve for

y

Solve

x, 2^{x} - 2^{y} = 1

220 = 2^{x}

x, 1 = e^{2 x - 3} - 5

5 = 5 + 16 e^{k (34)}

(\frac{1}{8})^{x} = 512