What is the answer to 7^x=8^{x-1} ?

The answer to 7^x=8^{x-1} is x=(3ln(2))/(3ln(2)-ln(7))

Solve for x: 7^x=8^{x-1}

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

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7^{x} = 8^{x - 1}

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

Decimal Notation

x = 15.57267 \dots

Solution steps

7^{x} = 8^{x - 1}

Apply exponent rules

x ln (7) = (x - 1) ln (8)

Solve

x ln (7) = (x - 1) ln (8) : x = \frac{3 ln ( 2 )}{3 ln ( 2 ) - ln ( 7 )}

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

7^{2 x} + 7^{x} - 6 = 0

7^{2 x} + 7^{x + 1} - 18 = 0

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

5 e^{- 2 t} = 6

m, 5^{n} + 5^{n} + 5^{n} + 5^{n} + 5^{n} = 5^{m}

What is the answer to 7^x=8^{x-1} ?
The answer to 7^x=8^{x-1} is x=(3ln(2))/(3ln(2)-ln(7))
Solve for x: 7^x=8^{x-1}
The solution is x=(3ln(2))/(3ln(2)-ln(7))