Answer:
x = 7/12
Step-by-step explanation:
Write the expression in exponential form with the base of 2
[tex]2x^{3x-3}[/tex] = [tex]32^{3x-2}[/tex]
[tex]2^{3x-3}[/tex] = [tex]2^{15x-10}[/tex]
Since the bases are the same, set the exponents equal
x - 3 = 15 - 10
Move variable to the left-hand side and change its sign
3x - 15x - 3 = -10
Move constant the the right-hand side and change its sign
3x - 15x = -10 + 3
Collect like terms
-12x = -10 + 3
Calculate the sum
-12x = -7
Divide both sides o the equation by -12
x = 7/12
Solution
7/12
Alternate form
x = 0.583
