What is the answer to (8191/8192)^x=0.5 ?

The answer to (8191/8192)^x=0.5 is x=(ln(0.5))/(ln(8191/8192))

Solve for x: (8191/8192)^x=0.5

The solution is x=(ln(0.5))/(ln(8191/8192))

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(\frac{8191}{8192})^{x} = 0.5

x = \frac{ln ( 0.5 )}{ln ( \frac{8191}{8192} )}

Decimal Notation

x = 5677.91512 \dots

Solution steps

(\frac{8191}{8192})^{x} = 0.5

Apply exponent rules

x ln (\frac{8191}{8192}) = ln (0.5)

Solve

x ln (\frac{8191}{8192}) = ln (0.5) : x = \frac{ln ( 0.5 )}{ln ( \frac{8191}{8192} )}

x = \frac{ln ( 0.5 )}{ln ( \frac{8191}{8192} )}

10 0^{x + 1} = 2 5^{x + 1}

7^{3 x} = 3^{2 - x}

x, 3^{2 x} + 2 \cdot 3^{x + 1} = 16

5^{2 x - 3} = 3^{3 x + 4}

2 x e^{x^{2}} = 0

What is the answer to (8191/8192)^x=0.5 ?
The answer to (8191/8192)^x=0.5 is x=(ln(0.5))/(ln(8191/8192))
Solve for x: (8191/8192)^x=0.5
The solution is x=(ln(0.5))/(ln(8191/8192))