What is the answer to 75=27^x ?

The answer to 75=27^x is x=(ln(75))/(3ln(3))

The solution is x=(ln(75))/(3ln(3))

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75=27^x

75 = 2 7^{x}

x = \frac{ln ( 75 )}{3 ln ( 3 )}

Decimal Notation

x = 1.30998 \dots

Solution steps

75 = 2 7^{x}

Apply exponent rules

ln (75) = x ln (27)

Solve

ln (75) = x ln (27) : x = \frac{ln ( 75 )}{3 ln ( 3 )}

x = \frac{ln ( 75 )}{3 ln ( 3 )}

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

e^{7 x} = 17

lo g_{10} (x^{l o g_{10} (x)}) = 1

e^{7 x} = 10

3^{x} = \frac{1}{5}