What is the answer to 4^x-4^{-2x}=3 ?

The answer to 4^x-4^{-2x}=3 is x=0.81701…

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

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

x = 0.81701 \dots

Solution steps

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

Apply exponent rules

4^{x} - (4^{x})^{- 2} = 3

Rewrite the equation with

4^{x} = u

u - (u)^{- 2} = 3

Solve

u - u^{- 2} = 3 : u \approx 3.10380 \dots

u \approx 3.10380 \dots

Substitute back

u = 4^{x},

solve for

x

Solve

4^{x} = 3.10380 \dots : x = 0.81701 \dots

x = 0.81701 \dots

14 (3 + e^{- x})^{- 1} = 3

100 e^{- 0.1 x} x = 0

3^{2 x + 1} = 28 (3^{x}) - 9

30 = 6 ln (1.8) (1. 8^{x})

(\frac{4}{5})^{\frac{1}{x}} = 3