Variables in Exponents

Jul 2010
1
0
I've been having problems with this equation:

\(\displaystyle x+3^x<4\)

I know the answer but not a non-graphical way to solve it. The best I can get is

\(\displaystyle x<log_3(4-x)\)

but can't seem to move all x to one side. Help would be appreciated!
 

skeeter

MHF Helper
Jun 2008
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6,765
North Texas
I've been having problems with this equation:

\(\displaystyle x+3^x<4\)

I know the answer but not a non-graphical way to solve it. The best I can get is

\(\displaystyle x<log_3(4-x)\)

but can't seem to move all x to one side. Help would be appreciated!
you will not be able to use elementary algebraic techniques to solve this inequality, however, note (by observation) that if \(\displaystyle x = 1\) , \(\displaystyle x + 3^x = 4\)

it should be fairly obvious that the solution set for the given inequality is \(\displaystyle x < 1\)
 
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