What is the answer to 75=33^x ?

The answer to 75=33^x is x=(ln(75))/(ln(33))

The solution is x=(ln(75))/(ln(33))

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75=33^x

75 = 3 3^{x}

x = \frac{ln ( 75 )}{ln ( 33 )}

Decimal Notation

x = 1.23480 \dots

Solution steps

75 = 3 3^{x}

Apply exponent rules

ln (75) = x ln (33)

Solve

ln (75) = x ln (33) : x = \frac{ln ( 75 )}{ln ( 33 )}

x = \frac{ln ( 75 )}{ln ( 33 )}

4^{x} = 3 (2)^{x}

3^{(1 + 2 x)} = 27

2^{n} = 40

3^{2 x + 5} = 81

e^{2 x} = e^{x} + 132