SOLUTION: Use logs (any base) to find the unknown: 2 to the power of 2x^2-3x = 2 to the power of x^2 - 2x + 12 (there are two answers, please find both using steps)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Use logs (any base) to find the unknown: 2 to the power of 2x^2-3x = 2 to the power of x^2 - 2x + 12 (there are two answers, please find both using steps)      Log On


   

Question 133343: Use logs (any base) to find the unknown:
2 to the power of 2x^2-3x = 2 to the power of x^2 - 2x + 12 (there are two answers, please find both using steps)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%5E%282x%5E2-3x%29=+2%5E%28x%5E2+-+2x+%2B+12%29 Start with the given equation


Since the bases are equal, this means that the exponents are equal.

2x%5E2-3x=x%5E2+-+2x+%2B+12 Set the exponents equal to one another


0=x%5E2-2x%2B12-2x%5E2%2B3x Subtract 2x%5E2 from both sides. Add 3x to both sides.


0=-x%5E2%2Bx%2B12 Combine like terms



0=-%28x-4%29%28x%2B3%29 Factor the right side


Now set each factor equal to zero:
x-4=0 or x%2B3=0

x=4 or x=-3 Now solve for x in each case


So our answers are

x=4 or x=-3