What is the answer to (2^{\sqrt[x]{5}})^4=32 ?

The answer to (2^{\sqrt[x]{5}})^4=32 is x=(ln(5))/(ln(5/4))

Solve for x: (2^{\sqrt[x]{5}})^4=32

The solution is x=(ln(5))/(ln(5/4))

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x = \frac{ln ( 5 )}{ln ( \frac{5}{4} )}

Decimal Notation

x = 7.21256 \dots

Solution steps

Apply exponent rules

\frac{1}{x} ln (5) = ln (\frac{5}{4})

Solve

\frac{1}{x} ln (5) = ln (\frac{5}{4}) : x = \frac{ln ( 5 )}{ln ( \frac{5}{4} )}

x = \frac{ln ( 5 )}{ln ( \frac{5}{4} )}

5^{x + 1} + 5^{x} = 150

2 e^{3 x} = 31

2^{x - 3} = 8^{x + 1}

x^{x} 2 + 2 x - 8 = 0

7^{2 x - 1} = 5^{x}

What is the answer to (2^{\sqrt[x]{5}})^4=32 ?
The answer to (2^{\sqrt[x]{5}})^4=32 is x=(ln(5))/(ln(5/4))
Solve for x: (2^{\sqrt[x]{5}})^4=32
The solution is x=(ln(5))/(ln(5/4))