What is the answer to 4*3^x=7*5^x ?

The answer to 4*3^x=7*5^x is x=(ln(7)-2ln(2))/(ln(3)-ln(5))

Solve for x: 4*3^x=7*5^x

The solution is x=(ln(7)-2ln(2))/(ln(3)-ln(5))

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4 \cdot 3^{x} = 7 \cdot 5^{x}

x = \frac{ln ( 7 ) - 2 ln ( 2 )}{ln ( 3 ) - ln ( 5 )}

Decimal Notation

x = - 1.09551 \dots

Solution steps

4 \cdot 3^{x} = 7 \cdot 5^{x}

Apply exponent rules

ln (4) + x ln (3) = ln (7) + x ln (5)

Solve

ln (4) + x ln (3) = ln (7) + x ln (5) : x = \frac{ln ( 7 ) - 2 ln ( 2 )}{ln ( 3 ) - ln ( 5 )}

x = \frac{ln ( 7 ) - 2 ln ( 2 )}{ln ( 3 ) - ln ( 5 )}

125 = 5^{x}

(1 5^{4 x + 3}) (9^{3 x - 5}) = 5

(1 + 0.01)^{x} = 2

1200 = 500 e^{k}

6 4^{2 x - 5} = 2^{3 - 7 x}

What is the answer to 4*3^x=7*5^x ?
The answer to 4*3^x=7*5^x is x=(ln(7)-2ln(2))/(ln(3)-ln(5))
Solve for x: 4*3^x=7*5^x
The solution is x=(ln(7)-2ln(2))/(ln(3)-ln(5))