Question

(1/9)^x=3*sqrt(27)
Solve for x, without log

Answer 1

Well, prime factorize both, I guess

Answer 2

\[
\frac{1}{9}=3^{-2}
\]And\[
3\sqrt{27} = 3^{1+\frac32}
\]

Answer 3

So \[
-2x=\frac 52
\]I guess

Answer 4

\(\large\color{black}{ (1/9)^x=3\sqrt{27} }\)

\(\large\color{black}{ (9)^{-x}=9\sqrt{3} }\)

\(\large\color{black}{ (9)^{-x-1}=\sqrt{3} }\)

\(\large\color{black}{ (9)^{-x-1}=9^{1/4}}\)

Answer 5

making sense?

Answer 6

I am getting the same result, I think.