What is the answer to 2^{(-x)}-2=4^x-1 ?

The answer to 2^{(-x)}-2=4^x-1 is x=-0.55146…

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

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

x = - 0.55146 \dots

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

(u)^{- 1} - 2 = (u)^{2} - 1

Solve

u^{- 1} - 2 = u^{2} - 1 : u \approx 0.68232 \dots

u \approx 0.68232 \dots

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 0.68232 \dots : x = - 0.55146 \dots

x = - 0.55146 \dots

3 6^{12 - m} = 6^{2 m}

3^{x} 4^{x + 2} = 8

3^{2 x - 5} = 81

6^{x} + \frac{36}{6 ^{x}} = 37

x, 9^{x + 1} + 1 = 10 (3^{x})

What is the answer to 2^{(-x)}-2=4^x-1 ?
The answer to 2^{(-x)}-2=4^x-1 is x=-0.55146…
Solve for x: 2^{(-x)}-2=4^x-1
The solution is x=-0.55146…