What is the answer to 5=8^x ?

The answer to 5=8^x is x=(ln(5))/(3ln(2))

The solution is x=(ln(5))/(3ln(2))

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5=8^x

5 = 8^{x}

x = \frac{ln ( 5 )}{3 ln ( 2 )}

Decimal Notation

x = 0.77397 \dots

Solution steps

5 = 8^{x}

Apply exponent rules

ln (5) = x ln (8)

Solve

ln (5) = x ln (8) : x = \frac{ln ( 5 )}{3 ln ( 2 )}

x = \frac{ln ( 5 )}{3 ln ( 2 )}

e^{x} + e^{- x} = 2 e

3^{(6 + 3 x)} = \frac{1}{27}

2 0^{x} = 4

5000 = 3^{n - 1}