What is the answer to 3^x= 3/2 ?

The answer to 3^x= 3/2 is x=(ln(3/2))/(ln(3))

Solve for x: 3^x= 3/2

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

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

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

Decimal Notation

x = 0.36907 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

63 = 1 9^{x}

2^{x + 3} = 5^{x - 1}

3^{- x + 1} = 4^{x + 2}

10 e^{8 x + 3} + 2 = 8

3^{x + 4} = 2 7^{2 x - 1}