What is the answer to 4^{2x}=32^{1/2} ?

The answer to 4^{2x}=32^{1/2} is x= 5/8

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4^{2x}=32^{1/2}

4^{2 x} = 3 2^{\frac{1}{2}}

x = \frac{5}{8}

Decimal Notation

x = 0.625

Solution steps

4^{2 x} = 3 2^{\frac{1}{2}}

Apply exponent rules

4 x = \frac{5}{2}

Solve

4 x = \frac{5}{2} : x = \frac{5}{8}

x = \frac{5}{8}

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

5^{x} = 60

(\frac{1}{2})^{x - 1} = 32

4^{2 x + 5} = 64

y, 6^{3} x 6^{5} = x^{y}