What is the answer to 3^{2x-3}=(27^{x+1})/2 ?

The answer to 3^{2x-3}=(27^{x+1})/2 is x=-(6ln(3)-ln(2))/(ln(3))

Solve for x: 3^{2x-3}=(27^{x+1})/2

The solution is x=-(6ln(3)-ln(2))/(ln(3))

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3^{2 x - 3} = \frac{2 7 ^{x + 1}}{2}

x = - \frac{6 ln ( 3 ) - ln ( 2 )}{ln ( 3 )}

Decimal Notation

x = - 5.36907 \dots

Solution steps

3^{2 x - 3} = \frac{2 7 ^{x + 1}}{2}

Multiply both sides by

2

3^{2 x - 3} \cdot 2 = \frac{2 7 ^{x + 1}}{2} \cdot 2

Simplify

3^{2 x - 3} \cdot 2 = 2 7^{x + 1}

Apply exponent rules

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

Solve

(2 x - 3) ln (3) + ln (2) = 3 (x + 1) ln (3) : x = - \frac{6 ln ( 3 ) - ln ( 2 )}{ln ( 3 )}

x = - \frac{6 ln ( 3 ) - ln ( 2 )}{ln ( 3 )}

e^{- 4 x} - 4 x e^{- 4 x} = 0

1 0^{a} = 92

2 \cdot 5^{x + 1} + 5^{x - 1} = 51

(\frac{1}{2})^{x + 1} = 8

x, r - 4 s + 4 t = e^{2 x + y}

What is the answer to 3^{2x-3}=(27^{x+1})/2 ?
The answer to 3^{2x-3}=(27^{x+1})/2 is x=-(6ln(3)-ln(2))/(ln(3))
Solve for x: 3^{2x-3}=(27^{x+1})/2
The solution is x=-(6ln(3)-ln(2))/(ln(3))