Question

What is the solution to the equation 9^(x - 1) = 27?

a) x = 2.5
b) x = 0.5
c) x = -0.5
d) x = -3.5

Answer 1

It would be x= 2.5 because before anything you would plug in a number such as 2.5 in for x and subtract one. You wouldn't put it to the nine yet. So it would be 9^(2.5-1)=27. Then once you subtracted it would equal 9^1.5=27. So lastly take 9 to the 1.5 power or 9^(1.5) and you get 27=27.

Answer 2

`9^(x - 1) = 27 \\ln(9^(x - 1)) = ln(27) \\(x - 1)ln(9) = ln(27) \\x - 1 = (ln(27))/(ln(9)) \\x = (ln(27))/(ln(9)) + 1 \\x = 2.5`

Thhe answer is equal to A. x = 2.5.