# Easy exponential equation but don't know how to solve properly.

• Apr 2nd 2012, 08:24 AM
freighter
Easy exponential equation but don't know how to solve properly.
Hi,

I have this simple exponential equation:

3^(x+2) + 3^(x-2) = 246

It is easy to see that the sum must be 243 + 3 = 3^5 + 3^1 and therefore x = 3.
But I haven't been able to solve it in the conventional way, using logarithms or some other method. Do you have any ideas to offer? Many thanks.
• Apr 2nd 2012, 08:33 AM
princeps
Re: Easy exponential equation but don't know how to solve properly.
Quote:

Originally Posted by freighter
Hi,

I have this simple exponential equation:

3^(x+2) + 3^(x-2) = 246

It is easy to see that the sum must be 243 + 3 = 3^5 + 3^1 and therefore x = 3.
But I haven't been able to solve it in the conventional way, using logarithms or some other method. Do you have any ideas to offer? Many thanks.

$\displaystyle 9\cdot 3^x+\frac{1}{9} \cdot 3^x=246$

$\displaystyle (9+\frac{1}{9})\cdot 3^x=246$

$\displaystyle \frac{82}{9} \cdot 3^x=246$

$\displaystyle 3^x=27$

$\displaystyle 3^x=3^3$

$\displaystyle x=3$
• Apr 2nd 2012, 08:34 AM
emakarov
Re: Easy exponential equation but don't know how to solve properly.
$\displaystyle 3^{x+2}+3^{x-2}=3^{x-2}(3^4+1)=3^{x-2}\cdot82=246$.
• Apr 2nd 2012, 09:04 AM
freighter
Re: Easy exponential equation but don't know how to solve properly.
Thanks, it's clear for me now :)