What is the answer to 5^{2x}=4 ?

The answer to 5^{2x}=4 is x=(ln(2))/(ln(5))

Solve for x: 5^{2x}=4

The solution is x=(ln(2))/(ln(5))

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5^{2 x} = 4

x = \frac{ln ( 2 )}{ln ( 5 )}

Decimal Notation

x = 0.43067 \dots

Solution steps

5^{2 x} = 4

Apply exponent rules

2 x ln (5) = ln (4)

Solve

2 x ln (5) = ln (4) : x = \frac{ln ( 2 )}{ln ( 5 )}

x = \frac{ln ( 2 )}{ln ( 5 )}

4^{- x} - 2^{- x + 2} + 4 = 0

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

7 e^{2 x + 3} = 20

4^{x} - 3 \cdot 2^{x + 2} + 32 = 0

27 = 3^{x + 1}