Question

solve logx27=3/2

Answer 1

2.1470?

Answer 2

in the back of the book it says the answer is 9

Answer 3

i dont know how to get 9

Answer 4

i know you first change it to the form 27=x3/2

Answer 5

but how do you solve it?

Answer 6

*You're not allowed to raise both sides of the equation by a fraction...*

Raise both sides by 2

(x^3/2)² = 27²

x^3 = 729

Transpose 729 to other side,

x^3 - 729 = 0

Factoring

(x - 9)(x² + 9x + 81) = 0

Theorem: If ab=0 then either a=0 or b=0

So either x - 9 = 0 or x² + 9x + 81 = 0 (2nd expression has imaginary roots)

x = 9

Answer 7

are you never allowed to do that?

Answer 8

and thanks!

Answer 9

you can but it will just take long to solve it.