What is the answer to 3^{x/5}=2^{4x-2} ?

The answer to 3^{x/5}=2^{4x-2} is x=(10ln(2))/(20ln(2)-ln(3))

Solve for x: 3^{x/5}=2^{4x-2}

The solution is x=(10ln(2))/(20ln(2)-ln(3))

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3^{\frac{x}{5}} = 2^{4 x - 2}

x = \frac{10 ln ( 2 )}{20 ln ( 2 ) - ln ( 3 )}

Decimal

x = 0.54303 \dots

Solution steps

3^{\frac{x}{5}} = 2^{4 x - 2}

Apply exponent rules

\frac{x}{5} ln (3) = (4 x - 2) ln (2)

Solve

\frac{x}{5} ln (3) = (4 x - 2) ln (2) : x = \frac{10 ln ( 2 )}{20 ln ( 2 ) - ln ( 3 )}

x = \frac{10 ln ( 2 )}{20 ln ( 2 ) - ln ( 3 )}

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

3 e^{x} + 7 = 9

5^{x} + 5^{x + 2} = 650

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

2 e^{3 x} = 5 e^{8 x}

What is the answer to 3^{x/5}=2^{4x-2} ?
The answer to 3^{x/5}=2^{4x-2} is x=(10ln(2))/(20ln(2)-ln(3))
Solve for x: 3^{x/5}=2^{4x-2}
The solution is x=(10ln(2))/(20ln(2)-ln(3))