What is the answer to 7^x=8 ?

The answer to 7^x=8 is x=(3ln(2))/(ln(7))

The solution is x=(3ln(2))/(ln(7))

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7^x=8

7^{x} = 8

x = \frac{3 ln ( 2 )}{ln ( 7 )}

Decimal Notation

x = 1.06862 \dots

Solution steps

7^{x} = 8

Apply exponent rules

x ln (7) = ln (8)

Solve

x ln (7) = ln (8) : x = \frac{3 ln ( 2 )}{ln ( 7 )}

x = \frac{3 ln ( 2 )}{ln ( 7 )}

8^{x} = 512

8 e^{2 x} - 43 e^{x} - 30 = 0

7 \cdot 3^{x} = 189

(5^{x})^{2} + 8 = 12 5^{2} x

15 - 0. 5^{x} = - 6