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

The answer to 5^{x-2}=3^{-x} is x=(2ln(5))/(ln(15))

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

The solution is x=(2ln(5))/(ln(15))

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

x = \frac{2 ln ( 5 )}{ln ( 15 )}

Decimal Notation

x = 1.18863 \dots

Solution steps

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

Apply exponent rules

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

Solve

(x - 2) ln (5) = - x ln (3) : x = \frac{2 ln ( 5 )}{ln ( 15 )}

x = \frac{2 ln ( 5 )}{ln ( 15 )}

5^{x} - 5^{- x} = 8

6^{x - 1} = 8^{2 - x}

6^{3 x + 2} = 3 6^{x - 6}

2 (5^{x}) = 32

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

What is the answer to 5^{x-2}=3^{-x} ?
The answer to 5^{x-2}=3^{-x} is x=(2ln(5))/(ln(15))
Solve for x: 5^{x-2}=3^{-x}
The solution is x=(2ln(5))/(ln(15))