What is the answer to 5^x= 2/5 ?

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

Solve for x: 5^x= 2/5

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

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5^{x} = \frac{2}{5}

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

Decimal Notation

x = - 0.56932 \dots

Solution steps

5^{x} = \frac{2}{5}

Apply exponent rules

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

Solve

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

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

x, x e^{y} + y e^{x} = 2

(\frac{1}{2})^{x} = 0.0625

5^{5 x + 2} = 45

5^{x + 1} = 1 0^{x}

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