What is the answer to 4^x=53 ?

The answer to 4^x=53 is x=(ln(53))/(2ln(2))

The solution is x=(ln(53))/(2ln(2))

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4^x=53

4^{x} = 53

x = \frac{ln ( 53 )}{2 ln ( 2 )}

Decimal Notation

x = 2.86396 \dots

Solution steps

4^{x} = 53

Apply exponent rules

x ln (4) = ln (53)

Solve

x ln (4) = ln (53) : x = \frac{ln ( 53 )}{2 ln ( 2 )}

x = \frac{ln ( 53 )}{2 ln ( 2 )}

6 4^{- x + 52} = 12 8^{x}

e^{- 6 x} = 0

5 e^{2 x} = 30

e^{x} = - 5 x

e^{2 x} + 5 e^{x} - 6 = 0