What is the answer to 10^x=5*10^{-x} ?

The answer to 10^x=5*10^{-x} is x=(ln(5))/(2ln(10))

Solve for x: 10^x=5*10^{-x}

The solution is x=(ln(5))/(2ln(10))

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1 0^{x} = 5 \cdot 1 0^{- x}

x = \frac{ln ( 5 )}{2 ln ( 10 )}

Decimal Notation

x = 0.34948 \dots

Solution steps

1 0^{x} = 5 \cdot 1 0^{- x}

Apply exponent rules

x ln (10) = ln (5) - x ln (10)

Solve

x ln (10) = ln (5) - x ln (10) : x = \frac{ln ( 5 )}{2 ln ( 10 )}

x = \frac{ln ( 5 )}{2 ln ( 10 )}

- 6 + 10 e^{- 2 x} = 9

2^{x + 3} + 4^{x + 1} - 320 = 0

9^{2 x} = \frac{1}{81}

7^{\frac{1}{x}} = 1 1^{x}

(2)^{3 x - 1} = 32

What is the answer to 10^x=5*10^{-x} ?
The answer to 10^x=5*10^{-x} is x=(ln(5))/(2ln(10))
Solve for x: 10^x=5*10^{-x}
The solution is x=(ln(5))/(2ln(10))