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

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

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

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

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

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

Decimal Notation

x = - 8.21439 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

75 \cdot 3^{x} = 375

9^{x} - 12 \times 3^{x} + 27 = 0

3^{2 x + 1} = 81

30 \cdot 3^{x} = 180

e^{2 x - 4} = 1

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