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anonymous
 one year ago
What is 27^(2x) = 9^(x3)
anonymous
 one year ago
What is 27^(2x) = 9^(x3)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes. Sorry I forgot to write that.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what's \(3^2=?\) and, say what's \(3^3=?\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can you explain how to get that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\large { {\color{brown}{ 27}}^{2x} = {\color{brown}{ 9}}^{x3}\qquad \begin{cases} 3^2\to {\color{brown}{ 9}}\\ 3^3\to {\color{brown}{ 27}} \end{cases}\qquad thus\implies (3^3)^{2x}=(3^2)^{x3} }\) see how to get "x" now?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Um...not exactly sure....Am I suppose to combine the 2x and x3?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\large { {\color{brown}{ 27}}^{2x} = {\color{brown}{ 9}}^{x3}\qquad \begin{cases} 3^2\to {\color{brown}{ 9}}\\ 3^3\to {\color{brown}{ 27}} \end{cases}\qquad thus\implies (3^3)^{2x}=(3^2)^{x3} \\ \quad \\ 3^{3\cdot (2x)}=3^{2\cdot (x3)}\impliedby \begin{array}{llll} \textit{same base, thus}\\\ \textit{exponents must also equal each other} \end{array}\\ \quad \\ 3(2x)=2(x3) }\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\large a^{whatever} = a^{whatever}\) means that whatever = whatever

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohh! So then: 6x=2x6 4x=6 x=2/3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\bf 6x=2x6\implies 4x=6\implies x=\cfrac{\cancel{6}}{\cancel{4}}\implies x=\cfrac{3}{2}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh whoops! Thanks for catching that!
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