# Equation solving

• Oct 11th 2011, 04:04 AM
sbhatnagar
Equation solving
Well I just need help solving this equation:$\displaystyle 5^{\frac{x}{2}}-2^x=1$
• Oct 11th 2011, 04:25 AM
earboth
Re: Equation solving
Quote:

Originally Posted by sbhatnagar
Well I just need help solving this equation:$\displaystyle 5^{\frac{x}{2}}-2^x=1$

1. By first inspection x = 2

2. Since $\displaystyle 5^{\tfrac x2}$ and $\displaystyle 2^x$ are both increasing continuously this solution must be the only one.
• Oct 11th 2011, 05:12 AM
sbhatnagar
Re: Equation solving
I know that x = 2 but can you show me the steps also?
• Oct 11th 2011, 06:19 AM
Prove It
Re: Equation solving
Quote:

Originally Posted by sbhatnagar
I know that x = 2 but can you show me the steps also?

You were told that this was just from inspection...
• Oct 11th 2011, 07:08 AM
HallsofIvy
Re: Equation solving
Quote:

Originally Posted by sbhatnagar
I know that x = 2 but can you show me the steps also?

The 'steps' are: $\displaystyle 5^{2/2}- 2^2= 5- 4= 1$.