What is the answer to 2^x=81 ?

The answer to 2^x=81 is x=(4ln(3))/(ln(2))

The solution is x=(4ln(3))/(ln(2))

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2^x=81

2^{x} = 81

x = \frac{4 ln ( 3 )}{ln ( 2 )}

Decimal Notation

x = 6.33985 \dots

Solution steps

2^{x} = 81

Apply exponent rules

x ln (2) = ln (81)

Solve

x ln (2) = ln (81) : x = \frac{4 ln ( 3 )}{ln ( 2 )}

x = \frac{4 ln ( 3 )}{ln ( 2 )}

2^{x} = 29

4 (8^{x}) = 64

(\frac{1}{2})^{x - 1} = 2^{3 x - 4}

6^{2 x} = 3 \cdot 2^{x}

x, 2^{x} = 5