What is the answer to 3^x=5^{2x-7} ?

The answer to 3^x=5^{2x-7} is x=(7ln(5))/(2ln(5)-ln(3))

Solve for x: 3^x=5^{2x-7}

The solution is x=(7ln(5))/(2ln(5)-ln(3))

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3^{x} = 5^{2 x - 7}

x = \frac{7 ln ( 5 )}{2 ln ( 5 ) - ln ( 3 )}

Decimal Notation

x = 5.31352 \dots

Solution steps

3^{x} = 5^{2 x - 7}

Apply exponent rules

x ln (3) = (2 x - 7) ln (5)

Solve

x ln (3) = (2 x - 7) ln (5) : x = \frac{7 ln ( 5 )}{2 ln ( 5 ) - ln ( 3 )}

x = \frac{7 ln ( 5 )}{2 ln ( 5 ) - ln ( 3 )}

6^{- 5 x - 7} = 70

8 e^{8 x} - e^{- x} = 0

2^{x + 1} = e^{1 - x}

e^{9 x} = 2

4^{2 x + 5} = 8^{3 x}

What is the answer to 3^x=5^{2x-7} ?
The answer to 3^x=5^{2x-7} is x=(7ln(5))/(2ln(5)-ln(3))
Solve for x: 3^x=5^{2x-7}
The solution is x=(7ln(5))/(2ln(5)-ln(3))