Logarithms and Exponents Question

[aquamarine08]

[SOLVED] Logarithms and Exponents Question

Homework Statement

$$5^{x}$$=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.

 

[Sourabh N]

Take log on both sides.

 

[stewartcs]

The only thing with this is that there isn't any power that 5 could be taken to, to get 41.

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

 

[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?

 

[aquamarine08]

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

 

[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!