What is the answer to x3^{(-3x-8)}=3^{(-6x+3)} ?

The answer to x3^{(-3x-8)}=3^{(-6x+3)} is x=(\W_{0}(531441ln(3)))/(3ln(3))

Solve for x: x3^{(-3x-8)}=3^{(-6x+3)}

The solution is x=(\W_{0}(531441ln(3)))/(3ln(3))

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x 3^{(- 3 x - 8)} = 3^{(- 6 x + 3)}

x = \frac{W _{0} ( 531441 ln ( 3 ) )}{3 ln ( 3 )}

Decimal Notation

x = 3.30404 \dots

Solution steps

x \cdot 3^{(- 3 x - 8)} = 3^{(- 6 x + 3)}

Subtract

3^{- 6 x + 3}

from both sides

x \cdot 3^{- 3 x - 8} - 3^{- 6 x + 3} = 3^{- 6 x + 3} - 3^{- 6 x + 3}

Simplify

x \cdot 3^{- 3 x - 8} - 3^{- 6 x + 3} = 0

Factor

x \cdot 3^{- 3 x - 8} - 3^{- 6 x + 3} : 9^{- (3 x + 4)} (2 7^{x} x - 177147)

9^{- (3 x + 4)} (2 7^{x} x - 177147) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

9^{- (3 x + 4)} = 0 or 2 7^{x} x - 177147 = 0

Solve

9^{- (3 x + 4)} = 0 :

No Solution for

x \in R

Solve

2 7^{x} x - 177147 = 0 : x = \frac{W _{0} ( 531441 ln ( 3 ) )}{3 ln ( 3 )}

x = \frac{W _{0} ( 531441 ln ( 3 ) )}{3 ln ( 3 )}

9^{3 x - 4} = 8 1^{2 x - 5}

2^{x} = 1080

2 = (1.025)^{x}

8 1^{y} 3^{- \frac{2 y}{3}} = 243

128 = 2 (2)^{x - 1}

What is the answer to x3^{(-3x-8)}=3^{(-6x+3)} ?
The answer to x3^{(-3x-8)}=3^{(-6x+3)} is x=(\W_{0}(531441ln(3)))/(3ln(3))
Solve for x: x3^{(-3x-8)}=3^{(-6x+3)}
The solution is x=(\W_{0}(531441ln(3)))/(3ln(3))