Math Help - logarithm #3

1. logarithm #3

3 ^ ( x+3 ) - 3 ^ ( x+2 ) = 2

2. Originally Posted by Zharif93
3 ^ ( x+3 ) - 3 ^ ( x+2 ) = 2
By inspection (or simply by intelligent trial-and-error) x = -2. That is the technique you would be expected to use if access to technology was not an option.

3. $3^{x+ 3}= 3^x3^3= 27(3^x)$. $3^{x+ 2}= 3^x3^2= 9(3^x)$.
Your equation is the same as $27(3^x)- 9(3^x)= (27- 9)3^x= 18(3^x)= 2$ so $3^x= \frac{2}{18}= \frac{1}{9}= 3^{-2}$.

I've always wondered about the phrase "using technology". It require technology to make a pencil doesn't it?

4. $3^{x+3}-3^{x+2}=3^{x+2}\left( 3-1 \right)=2,$ that's all.