Question

Hi,
I cannot figure this equation out... 5*3^(3x)-9^(x+2)=0, so far I have come up with this 5*3^(3x)-9^(x+2)=0 <=> 3^(3x)-9^(x+2)/5=0 <=> 3^(3x)=9^(x+2)/5 <=> log_3(3x)=log_3(9^(x+2)/5) <=> 3x=ln(9^(x+2)/5)/ln3, and now I am stuck :( could you please help me?

Answer 1

\[5*3^{3x}-9^{x+2}=0\]
\[5*(3^{3})^x-9^{x}*81=0\]
\[27^x=9^x16.2\]

Answer 2

\[9^x=(3^2)^x=3^{3x}*3^{-x}=27^x*3^{-x}\]

Answer 3

\[1=3^{-x}16.2\]

Answer 4

\[3^x=16.2\]

Answer 5

\[x=\log_3(16.2)\]

Answer 6

Thank you!