SOLUTION: (27) ^2x+1 = 3^-1. Solve for x. Choose one answer. a. 2/3 b. No solution c. 3/2 d. -2/3 e. -3/2

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: (27) ^2x+1 = 3^-1. Solve for x. Choose one answer. a. 2/3 b. No solution c. 3/2 d. -2/3 e. -3/2      Log On


   

Question 763313: (27) ^2x+1 = 3^-1. Solve for x.
Choose one answer.
a. 2/3
b. No solution
c. 3/2
d. -2/3
e. -3/2
Found 2 solutions by MathLover1, algebrahouse.com:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

27%5E%282x%2B1%29+=+3%5E-1...write is same base 27%5E%282x%2B1%29+=+3%5E%283%282x%2B1%29%29=+3%5E%286x%2B3%29
3%5E%286x%2B3%29+=+3%5E-1.....if bases same, exponents same too

6x%2B3+=-1
6x=-1-3
6x=-4...divide by 2
6x%2F2=-4%2F2
3x=-2
x=-2%2F3

so, answer is: d. -2%2F3

Answer by algebrahouse.com(1659) About Me  (Show Source):
You can put this solution on YOUR website!
27^(2x + 1) = 3^-1
3^3(2x + 1) = 3^-1 {changed 27 to have a base of 3}
3(2x + 1) = -1 {since bases are equal, set exponents equal to each other}
6x + 3 = -1 {used distributive property}
6x = -4 {subtracted 3 from each side}
x = -2/3 {divided each side by 6 and reduced}

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