What is the answer to (2/3)^x=5^{x-1} ?

The answer to (2/3)^x=5^{x-1} is x=(ln(5))/(ln(5)-ln(2/3))

Solve for x: (2/3)^x=5^{x-1}

The solution is x=(ln(5))/(ln(5)-ln(2/3))

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(\frac{2}{3})^{x} = 5^{x - 1}

x = \frac{ln ( 5 )}{ln ( 5 ) - ln ( \frac{2}{3} )}

Decimal Notation

x = 0.79876 \dots

Solution steps

(\frac{2}{3})^{x} = 5^{x - 1}

Apply exponent rules

x ln (\frac{2}{3}) = (x - 1) ln (5)

Solve

x ln (\frac{2}{3}) = (x - 1) ln (5) : x = \frac{ln ( 5 )}{ln ( 5 ) - ln ( \frac{2}{3} )}

x = \frac{ln ( 5 )}{ln ( 5 ) - ln ( \frac{2}{3} )}

3^{x + 2} + 3^{2 - x} = 82

2 0^{x - 9} = 12

1 0^{\frac{3 x - 1}{2 x + 1}} = 100

0.2 e^{4 x} - 0.1 e^{- 3 x} = 0

(1 4^{3 x + 1}) (8^{2 x + 3}) = 7

What is the answer to (2/3)^x=5^{x-1} ?
The answer to (2/3)^x=5^{x-1} is x=(ln(5))/(ln(5)-ln(2/3))
Solve for x: (2/3)^x=5^{x-1}
The solution is x=(ln(5))/(ln(5)-ln(2/3))