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

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

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

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

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

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

Decimal Notation

x = 6.30132 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

3^{x + 2} - 3^{x} = 72

8^{x} - 4^{x} - 2^{x} + 1 + 2 = 0

30 = 69.42 \cdot 0.9 7^{x}

2 \cdot x - 4 \cdot e^{- x} = 0

\frac{5 ^{3 n}}{( 5 ^{6} )} = 5^{3}

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