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

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

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

The solution is x=(2ln(15))/(ln(5)-3ln(3))

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

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

Decimal Notation

x = - 3.21163 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

3^{2 x} = 9

2^{5 x} = 3^{2 x + 1}

2^{x - 1} = 1

81 = 3^{x}

3^{2 x} = 27

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