What is the answer to 3*2^{3x}=7*3^{3x-2} ?

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

Solve for x: 3*2^{3x}=7*3^{3x-2}

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

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

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

Decimal Notation

x = 1.10977 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

(3^{2 x + 1} + 9) = (3^{x + 3} + 3^{x})

3^{x} + 3^{x - 1} + 3^{x - 2} = 13

e^{2 x} - 2 e^{x} = 1

1 6^{x} = 8^{2 x + 3}

lo g_{10} (43) = 4. 2^{x}

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