What is the answer to 4^{2x+1}=8^{4x} ?

The answer to 4^{2x+1}=8^{4x} is x= 1/4

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4^{2x+1}=8^{4x}

4^{2 x + 1} = 8^{4 x}

x = \frac{1}{4}

Decimal Notation

x = 0.25

Solution steps

4^{2 x + 1} = 8^{4 x}

Apply exponent rules

2 (2 x + 1) = 12 x

Solve

2 (2 x + 1) = 12 x : x = \frac{1}{4}

x = \frac{1}{4}

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

2 = 3 e^{4 x}

\frac{1}{e ^{x}} = e^{- x}

e^{x + 5} = 5

3^{x} - 14 \cdot 3^{- x} = 5