What is the answer to 2^{-x}=5 ?

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

Solve for x: 2^{-x}=5

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

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2^{- x} = 5

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

Decimal Notation

x = - 2.32192 \dots

Solution steps

2^{- x} = 5

Apply exponent rules

- x ln (2) = ln (5)

Solve

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

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

(e^{4})^{x} (e^{x})^{2} = e^{1} 2

5^{2 x - 1} = 5

3^{x - 2} = 9

6 4^{x} = 16

2 7^{5 x - 6} = 9^{7 x + 3}