What is the answer to 2*3^x=7*5^x ?

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

Solve for x: 2*3^x=7*5^x

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

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

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

Decimal Notation

x = - 2.45242 \dots

Solution steps

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

Apply exponent rules

ln (2) + x ln (3) = ln (7) + x ln (5)

Solve

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

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

129 6^{3 x - 3} = 21 6^{3 x - 5}

2 0^{- 2 x + 3} = 4^{3 x - 1} \cdot 5^{- x + 4}

2^{x - 4} = 3 2^{x + 4}

5^{- x + 2} = 1 1^{7 x}

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

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