What is the answer to 3^x=0.5 ?

The answer to 3^x=0.5 is x=(ln(0.5))/(ln(3))

The solution is x=(ln(0.5))/(ln(3))

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3^x=0.5

3^{x} = 0.5

x = \frac{ln ( 0.5 )}{ln ( 3 )}

Decimal Notation

x = - 0.63092 \dots

Solution steps

3^{x} = 0.5

Apply exponent rules

x ln (3) = ln (0.5)

Solve

x ln (3) = ln (0.5) : x = \frac{ln ( 0.5 )}{ln ( 3 )}

x = \frac{ln ( 0.5 )}{ln ( 3 )}

(\frac{8}{27})^{2 - 3 x} = 1

3^{4 x} = \frac{1}{27}

3 \cdot 3^{2 x} - 4 \cdot 3^{x} = - 1

3^{x + 2} - 3^{x} = \frac{8}{27}

6^{2 x} = 7