Need help with a simple problem 2^x=3^x+1

Question

asked Apr 28, 2018 100k views

1 Answer

Terry Zhang · Answer 1 · 2018-05-03T17:59:37+0000

For
$x\ \textgreater \ 0$ ,
$2^x\ \textless \ 3^x$ , all the more
$2^x\ \textless \ 3^x+1$ , therefore no solution.

For
x=0

, we have
$2^0=3^0+1 \Rightarrow 1=1+1 \Rightarrow 1=2$ . Obviously that' false.

For
$x\ \textless \ 0$ both
2^x

and

, where
$2^x\ \textgreater \ 3^x$ , belong to the range
(0,1)

, then

belong to the range
(1,2)

.
Those ranges don't have a common part, therefore, again, no solution.

So, the equation
2^x=3^x+1

doesn't have a solution.