What is the answer to 81=33^x ?

The answer to 81=33^x is x=(4ln(3))/(ln(33))

The solution is x=(4ln(3))/(ln(33))

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81=33^x

81 = 3 3^{x}

x = \frac{4 ln ( 3 )}{ln ( 33 )}

Decimal Notation

x = 1.25681 \dots

Solution steps

81 = 3 3^{x}

Apply exponent rules

ln (81) = x ln (33)

Solve

ln (81) = x ln (33) : x = \frac{4 ln ( 3 )}{ln ( 33 )}

x = \frac{4 ln ( 3 )}{ln ( 33 )}

4^{- x} = 256

8^{2 x} = 4^{x - 1}

e^{t} = 687

3^{7 x} = 8 1^{4 - 2 x}

7^{x} = \frac{1}{7}