Question

How do you evaluate `log_9 x=3/2`?

Answer 1

`x=27`

Explanation:

Remember that in general `log_b a = c` means `b^c=a`
(You really need to memorize this; it's a basic definition.)

Therefore `log_9 x=3/2`
means
`color(white)("XXX")9^(3/2)=x`

`rarrcolor(white)("XX")x=9^(3/2)`

`color(white)("XXXX")=(9^(1/2))^3`

`color(white)("XXXX")=(+3)^3` (the negative root can be ignored since log arguments must be positive)

`color(white)("XXXX")=27`