What is the answer to 5^{7x+4}=3^{x+2} ?

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

Solve for x: 5^{7x+4}=3^{x+2}

The solution is x=(2ln(3)-4ln(5))/(7ln(5)-ln(3))

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5^{7 x + 4} = 3^{x + 2}

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

Decimal Notation

x = - 0.41706 \dots

Solution steps

5^{7 x + 4} = 3^{x + 2}

Apply exponent rules

(7 x + 4) ln (5) = (x + 2) ln (3)

Solve

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

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

e^{- 5 x} = 10

6 4^{x} - 8^{x} - 56 = 0

e^{x} + 4 e^{- x} = 5

b^{x}

6 4^{x^{2}} = 25 6^{x}

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