Question

(1/3)^x-3 = 9

Answer 1

(1/3)^(x-3)=9
(1/3)^(x-3)=3^2
(1/3)^(x-3)=(1/3)^(-2)
=>x-3=-2
=>x=1

Answer 2

\[\left(\frac{1}{3}\right)^x-3=9\]
\[\left(\frac{1}{3}\right)^x=12\]
\[x\phantom{.}\log_{10}\left(\frac{1}{3}\right)=\log_{10}12\]
\[x=\frac{\log_{10}{12}}{\log_{10}(1/3)}\]
\[x=\frac{\log_{10}12}{\log_{10}1-\log_{10}3}\]
\[x=-\frac{\log_{10}12}{\log_{10}3}\approx2.26\]

Answer 3

Wait....im noticing that me and @sauravshakya 's answer is different...is the equation A or B:
\[\eqalign{
&A.\phantom{spce}\left(\frac{1}{2}\right)^x-3=9 \\
&B.\phantom{spce}\left(\frac{1}{2}\right)^{x-3}=9 \\
}\]

Answer 4

B :D

Answer 5

Haha WOOOOW...k. wait.

Answer 6

and its 1/3

Answer 7

Err yeah haha

Answer 8

k.
\[\eqalign{
&\left(\frac{1}{3}\right)^{x-3}=9 \\
&(3^{-1})^{x-3}=9 \\
&(x-3)\log_{3}3^{-1}=\log_{3}9 \\
&(x-3)(-1)=2 \\
&3-x=2 \\
&x=1
}\]
To prove it:
\[\eqalign{
&\left(\frac{1}{3}\right)^{x-3}=9 \\
&\left(\frac{1}{3}\right)^{1-3}=9 \\
&\left(\frac{1}{3}\right)^{-2}=9 \\
&\left[3^{(-1)}\right]^{-2}=9 \\
&3^{(-1\times-2)}=9 \\
&3^2=9 \\
&9=9 \\
}\]
So, \(LS=RS \therefore QED\).