What is the answer to 4*3^x=12*5^x ?

The answer to 4*3^x=12*5^x is x=(ln(3))/(ln(3)-ln(5))

Solve for x: 4*3^x=12*5^x

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

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4 \cdot 3^{x} = 12 \cdot 5^{x}

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

Decimal Notation

x = - 2.15066 \dots

Solution steps

4 \cdot 3^{x} = 12 \cdot 5^{x}

Apply exponent rules

ln (4) + x ln (3) = ln (12) + x ln (5)

Solve

ln (4) + x ln (3) = ln (12) + x ln (5) : x = \frac{ln ( 3 )}{ln ( 3 ) - ln ( 5 )}

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

e^{2 x} - 14 e^{x} + 13 = 0

3^{2 x - 1} - 8 \times 3^{x - 1} = 3

1 0^{4 x} = 72

6^{5 x} = 3000

e^{6 x} - 9 e^{3 x} - 18 = 0

What is the answer to 4*3^x=12*5^x ?
The answer to 4*3^x=12*5^x is x=(ln(3))/(ln(3)-ln(5))
Solve for x: 4*3^x=12*5^x
The solution is x=(ln(3))/(ln(3)-ln(5))