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

The answer to 3*2^x=5^{x-2} is x=(ln(75))/(ln(5)-ln(2))

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

The solution is x=(ln(75))/(ln(5)-ln(2))

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

x = \frac{ln ( 75 )}{ln ( 5 ) - ln ( 2 )}

Decimal Notation

x = 4.71191 \dots

Solution steps

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

Apply exponent rules

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

Solve

ln (3) + x ln (2) = (x - 2) ln (5) : x = \frac{ln ( 75 )}{ln ( 5 ) - ln ( 2 )}

x = \frac{ln ( 75 )}{ln ( 5 ) - ln ( 2 )}

3 \cdot 2^{x} = 5^{x - 1}

5^{2 x + 6} = 1

(x + 3)^{(x + 3)} = 1 1^{6} 0.1 1^{5}

2^{2 x - 6} = 1

\frac{3 π}{2} (8) = x e^{x}

What is the answer to 3*2^x=5^{x-2} ?
The answer to 3*2^x=5^{x-2} is x=(ln(75))/(ln(5)-ln(2))
Solve for x: 3*2^x=5^{x-2}
The solution is x=(ln(75))/(ln(5)-ln(2))