What is the answer to 2^{-x}-ln(2)*2^{-x}x=0 ?

The answer to 2^{-x}-ln(2)*2^{-x}x=0 is x= 1/(ln(2))

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2^{-x}-ln(2)*2^{-x}x=0

2^{- x} - ln (2) \cdot 2^{- x} x = 0

x = \frac{1}{ln ( 2 )}

Decimal Notation

x = 1.44269 \dots

Solution steps

2^{- x} - ln (2) \cdot 2^{- x} x = 0

Factor

2^{- x} (1 - ln (2) x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2^{- x} = 0 or 1 - ln (2) x = 0

Solve

2^{- x} = 0 :

No Solution for

x \in R

Solve

1 - ln (2) x = 0 : x = \frac{1}{ln ( 2 )}

x = \frac{1}{ln ( 2 )}

2 7^{a} = 8

2 \cdot 5^{x} = 250

8 (1 0^{3 x}) = 12

2 = (1 + \frac{11}{200})^{n}

x^{2} 2^{x} - 2^{x} 18 = 0

What is the answer to 2^{-x}-ln(2)*2^{-x}x=0 ?
The answer to 2^{-x}-ln(2)*2^{-x}x=0 is x= 1/(ln(2))
Solve for x: 2^{-x}-ln(2)*2^{-x}x=0
The solution is x= 1/(ln(2))