What is the answer to 5^{3x+2}=11^{7x-2} ?

The answer to 5^{3x+2}=11^{7x-2} is x=(2ln(55))/(7ln(11)-3ln(5))

Solve for x: 5^{3x+2}=11^{7x-2}

The solution is x=(2ln(55))/(7ln(11)-3ln(5))

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5^{3 x + 2} = 1 1^{7 x - 2}

x = \frac{2 ln ( 55 )}{7 ln ( 11 ) - 3 ln ( 5 )}

Decimal Notation

x = 0.67029 \dots

Solution steps

5^{3 x + 2} = 1 1^{7 x - 2}

Apply exponent rules

(3 x + 2) ln (5) = (7 x - 2) ln (11)

Solve

(3 x + 2) ln (5) = (7 x - 2) ln (11) : x = \frac{2 ln ( 55 )}{7 ln ( 11 ) - 3 ln ( 5 )}

x = \frac{2 ln ( 55 )}{7 ln ( 11 ) - 3 ln ( 5 )}

\frac{4 ^{x - 1}}{2 ^{x + 2}} = 256

2 7^{- x - 1} = 81

e^{- \frac{1}{2} x^{2}} = 0

8 1^{x} = 3^{4 x}

(1.07)^{x} = 2

What is the answer to 5^{3x+2}=11^{7x-2} ?
The answer to 5^{3x+2}=11^{7x-2} is x=(2ln(55))/(7ln(11)-3ln(5))
Solve for x: 5^{3x+2}=11^{7x-2}
The solution is x=(2ln(55))/(7ln(11)-3ln(5))