What is the answer to 5^{2x}=8 ?

The answer to 5^{2x}=8 is x=(3ln(2))/(2ln(5))

Solve for x: 5^{2x}=8

The solution is x=(3ln(2))/(2ln(5))

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5^{2 x} = 8

x = \frac{3 ln ( 2 )}{2 ln ( 5 )}

Decimal Notation

x = 0.64601 \dots

Solution steps

5^{2 x} = 8

Apply exponent rules

2 x ln (5) = ln (8)

Solve

2 x ln (5) = ln (8) : x = \frac{3 ln ( 2 )}{2 ln ( 5 )}

x = \frac{3 ln ( 2 )}{2 ln ( 5 )}

e^{2 x} - 13 e^{x} + 42 = 0

e^{6 x - 5} = 19

x, e^{2 x + 2 y + z} = 1

y, e^{y} = 0

y, e^{y} = 9