Question

What is 27^(2x) = 9^(x-3)

Answer 1

do you need x?

Answer 2

Yes. Sorry I forgot to write that.

Answer 3

x=-3/2

Answer 4

what's \(3^2=?\) and, say what's \(3^3=?\)

Answer 5

Can you explain how to get that?

Answer 6

\(\large {
{\color{brown}{ 27}}^{2x} = {\color{brown}{ 9}}^{x-3}\qquad
\begin{cases}
3^2\to {\color{brown}{ 9}}\\
3^3\to {\color{brown}{ 27}}
\end{cases}\qquad thus\implies (3^3)^{2x}=(3^2)^{x-3}
}\)

see how to get "x" now?

Answer 7

Um...not exactly sure....Am I suppose to combine the 2x and x-3?

Answer 8

\(\large {
{\color{brown}{ 27}}^{2x} = {\color{brown}{ 9}}^{x-3}\qquad
\begin{cases}
3^2\to {\color{brown}{ 9}}\\
3^3\to {\color{brown}{ 27}}
\end{cases}\qquad thus\implies (3^3)^{2x}=(3^2)^{x-3}
\\ \quad \\
3^{3\cdot (2x)}=3^{2\cdot (x-3)}\impliedby
\begin{array}{llll}
\textit{same base, thus}\\\
\textit{exponents must also equal each other}

\end{array}\\ \quad \\
3(2x)=2(x-3)
}\)

Answer 9

\(\large a^{whatever} = a^{whatever}\) means that whatever = whatever

Answer 10

Ohh! So then:
6x=2x-6
4x=-6
x=-2/3

Answer 11

Is that right?

Answer 12

yeap

Answer 13

hmmm actually wait

Answer 14

Thanks!

Answer 15

\(\bf 6x=2x-6\implies 4x=-6\implies x=-\cfrac{\cancel{6}}{\cancel{4}}\implies x=-\cfrac{3}{2}\)

Answer 16

Oh whoops! Thanks for catching that!