What is the answer to 7^{2x+1}=3^{x+2} ?

The answer to 7^{2x+1}=3^{x+2} is x=(2ln(3)-ln(7))/(2ln(7)-ln(3))

Solve for x: 7^{2x+1}=3^{x+2}

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

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

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

Decimal Notation

x = 0.08997 \dots

Solution steps

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

Apply exponent rules

(2 x + 1) ln (7) = (x + 2) ln (3)

Solve

(2 x + 1) ln (7) = (x + 2) ln (3) : x = \frac{2 ln ( 3 ) - ln ( 7 )}{2 ln ( 7 ) - ln ( 3 )}

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

e^{6 x} = 6 e^{x}

t, x = e^{- t}

3^{x} \cdot 3^{x + 1} = 9

3 e^{x} = 4 e^{- 3 x}

4 = 1.0 5^{x}

What is the answer to 7^{2x+1}=3^{x+2} ?
The answer to 7^{2x+1}=3^{x+2} is x=(2ln(3)-ln(7))/(2ln(7)-ln(3))
Solve for x: 7^{2x+1}=3^{x+2}
The solution is x=(2ln(3)-ln(7))/(2ln(7)-ln(3))