What is the answer to 3^{x-2}=5^{2x+1} ?

The answer to 3^{x-2}=5^{2x+1} is x=(ln(45))/(ln(3)-2ln(5))

Solve for x: 3^{x-2}=5^{2x+1}

The solution is x=(ln(45))/(ln(3)-2ln(5))

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

x = \frac{ln ( 45 )}{ln ( 3 ) - 2 ln ( 5 )}

Decimal Notation

x = - 1.79537 \dots

Solution steps

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

Apply exponent rules

(x - 2) ln (3) = (2 x + 1) ln (5)

Solve

(x - 2) ln (3) = (2 x + 1) ln (5) : x = \frac{ln ( 45 )}{ln ( 3 ) - 2 ln ( 5 )}

x = \frac{ln ( 45 )}{ln ( 3 ) - 2 ln ( 5 )}

6^{2 x} - 42 (6^{x}) + 216 = 0

y, e^{x^{2} y} = x + y

10 = 0.1 7^{- x}

2^{x - 2} = 5

5^{100} - 5^{99} = 4 \cdot 5^{x}

What is the answer to 3^{x-2}=5^{2x+1} ?
The answer to 3^{x-2}=5^{2x+1} is x=(ln(45))/(ln(3)-2ln(5))
Solve for x: 3^{x-2}=5^{2x+1}
The solution is x=(ln(45))/(ln(3)-2ln(5))