What is the answer to 1/3 =2^x ?

The answer to 1/3 =2^x is x=-(ln(3))/(ln(2))

Solve for x: 1/3 =2^x

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

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\frac{1}{3} = 2^{x}

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

Decimal Notation

x = - 1.58496 \dots

Solution steps

\frac{1}{3} = 2^{x}

Apply exponent rules

ln (\frac{1}{3}) = x ln (2)

Solve

ln (\frac{1}{3}) = x ln (2) : x = - \frac{ln ( 3 )}{ln ( 2 )}

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

lo g_{4} (2^{4 x}) = 2^{l o g_{2} (4)}

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

5^{x} + 2 = 625

(\frac{1}{4})^{2 x - 2} = 256

1 6^{x} + 2 0^{x} = 2 0^{x}