What is the answer to 85=27^x ?

The answer to 85=27^x is x=(ln(85))/(3ln(3))

The solution is x=(ln(85))/(3ln(3))

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85=27^x

85 = 2 7^{x}

x = \frac{ln ( 85 )}{3 ln ( 3 )}

Decimal Notation

x = 1.34795 \dots

Solution steps

85 = 2 7^{x}

Apply exponent rules

ln (85) = x ln (27)

Solve

ln (85) = x ln (27) : x = \frac{ln ( 85 )}{3 ln ( 3 )}

x = \frac{ln ( 85 )}{3 ln ( 3 )}

(\frac{1}{3})^{2 x} = 81

4^{x - 3} = 5

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

2^{2 n} = 4^{n}

12 x \cdot 3^{x + 1} = 648