4^(2X)=10: solve for value of X in exponent

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
llshearer
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4^(2X)=10: solve for value of X in exponent

Postby llshearer » Wed Jul 29, 2009 9:14 pm

I'm 33 and this is a college 'easy' math course I'm taking. I'm completely unclear as to how one would go about finding the value for X in an exponent.

4^(2X)=10

I know you're supposed to use LOG but I don't even understand how to use my calculator! I'm dying here, so if you can help me, your streets in Heaven will be paved with gold!

Thank you so very much,
Laurie

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stapel_eliz
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Postby stapel_eliz » Wed Jul 29, 2009 9:48 pm

We can't explain your calculator to you; you'll need to read your owner's manual for that. :oops:

Are you familiar with logs at all, so we might be able to work with you on the algebra?

Thank you! :D


kklecan
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Re: 4^(2X)=10: solve for value of X in exponent

Postby kklecan » Sat Aug 22, 2009 2:07 am

llshearer wrote:I'm 33 and this is a college 'easy' math course I'm taking. I'm completely unclear as to how one would go about finding the value for X in an exponent.

4^(2X)=10



Laurie,
First of all, don't be too hard on yourself. Logs aren't "easy" for most people when they study them. Your course may already be over; if so, sorry for rehashing.

There are two schools of thought on using logs to solve equations like this. Some use the definition of a log to rewrite the equation in log form. This first step is usually pretty quick, but then you get stuck with a log your calculator can't perform (at least, in my case. Mine only does log-base-10 and log-base-e.) There's a formula that will help you with that, the change-of-base formula. I'm sure you can find it in the "lessons" section here...

Others take the log of both sides and use some of the "properties of logs" that are probably listed in your textbook to simplify. That's the method used by the last poster, michaelempeigne.

If you're still working on this, maybe you could let us know which method you're more familiar with, and we can nudge you in the right direction. Good luck!

AmySaunders
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Re: 4^(2X)=10: solve for value of X in exponent

Postby AmySaunders » Tue Aug 25, 2009 11:39 pm

Use a log base 10. :lol:

Here are the steps. :idea:

4^2x=10
2x log^10 4=10
2x=10/log 4
x=(10/ log 4) /2

:shock: But I am 12, so I could be wrong

QM deFuturo
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Re: 4^(2X)=10: solve for value of X in exponent

Postby QM deFuturo » Wed Aug 26, 2009 1:26 am

AmySaunders wrote:Use a log base 10. :lol:

Here are the steps. :idea:

4^2x=10
2x log^10 4=10
2x=10/log 4
x=(10/ log 4) /2

:shock: But I am 12, so I could be wrong


In math and science, your age is not important. The right answer is the right answer, no matter how old you are.

In your case though, you forgot to take the log of BOTH sides of the equation. You can solve this problem in two different ways. I think the easiest is to take the common log of both sides, like (I think) you tried to do, but forgot to do for the right side.







My calculator tells me

so I get x = 0.83048

You could also use the definition of the log to solve the problem:




Since most calculators don't have a log base "4" key, you use change of base formula:

substituting this changed log back into the previous equation give us


which is the same answer as we got in the first method of solving this problem.

QM


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