# Logarithms and Exponents Question

1. Jan 7, 2008

### aquamarine08

[SOLVED] Logarithms and Exponents Question

The problem statement, all variables and given/known data

$$5^{x}$$=41

The attempt at a solution

Well, I know that one way to figure this out would be that to find a common base for both sides of the equation and then use the known exponent to find the variable. The only thing with this is that there isn't any power that 5 could be taken to, to get 41. Please help...I know this is a simple question but I just can't get it.

2. Jan 7, 2008

### Sourabh N

Take log on both sides.

3. Jan 7, 2008

### stewartcs

Sure there is. Don't limit your thinking to whole numbers.

4. Jan 7, 2008

### symbolipoint

More precisely;
find logarithm of both sides with either common logs or natural logs. Take your pick. Just use the same for both sides.

You then have your choice of using a table of logarithms or a good scientific calculator.
Process starts like this:
$$$\begin{array}{l} \log (5)^x = \log (41) \\ x\log (5) = \log (41) \\ \end{array}$$$

Can you take the process from there?

5. Jan 8, 2008

### aquamarine08

yep...i got it ! thanks everyone for ur help!

6. Jan 9, 2008

### unplebeian

I like Stewartcs's solution better. Taking ln on both sides is a very easy way. This idea is thinking outside the box or he is thinking unlike the standard way. This deserves credit. Way to go, Stewartcs's!