What is the answer to 3^x= 1/5 ?

The answer to 3^x= 1/5 is x=-(ln(5))/(ln(3))

Solve for x: 3^x= 1/5

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

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3^{x} = \frac{1}{5}

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

Decimal Notation

x = - 1.46497 \dots

Solution steps

3^{x} = \frac{1}{5}

Apply exponent rules

x ln (3) = ln (\frac{1}{5})

Solve

x ln (3) = ln (\frac{1}{5}) : x = - \frac{ln ( 5 )}{ln ( 3 )}

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

3^{x} = \frac{1}{8}

e^{20 \cdot l n (x)} = e^{- 3}

e^{2 x - 3} = 37

8 = 6^{x + 4}

e^{(- 0.2 t)} = 25