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

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

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
llshearer

Posts: 1
Joined: Wed Jul 29, 2009 9:10 pm

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

Thank you!

stapel_eliz

Posts: 1804
Joined: Mon Dec 08, 2008 4:22 pm

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

$4^{2x} = 10$
$2x ln 4 = ln 10$
$2x = \frac {ln 10}{ln 4}$
$x = \frac{ln 10}{2 ln 4}$
michaelempeigne

Posts: 6
Joined: Wed Aug 05, 2009 1:20 pm

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

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!
kklecan

Posts: 3
Joined: Thu Aug 20, 2009 4:13 am

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

Use a log base 10.

Here are the steps.

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

But I am 12, so I could be wrong
AmySaunders

Posts: 34
Joined: Thu Aug 20, 2009 6:27 pm

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

AmySaunders wrote:Use a log base 10.

Here are the steps.

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

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.

$4^{2x} = 10$
$log_{10} 4^{2x} = log_{10} 10$
$2x log_{10} 4 = 1$
$2x = \frac{1}{ log_{10} 4}$
$x = \frac{1}{2 log_{10} 4}$

My calculator tells me
$log_{10} 4 = 0.60206$
so I get x = 0.83048

You could also use the definition of the log to solve the problem:
$4^{2x} = 10$
$2x = log_{4} 10$
$x = \frac{log_{4} 10}{2}$

Since most calculators don't have a log base "4" key, you use change of base formula:
$log_{4} 10 = \frac{log_{10} 10}{log_{10} 4} = \frac{1}{log_{10} 4}$
substituting this changed log back into the previous equation give us
$x = \frac{1}{2 log_{10} 4}$

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

QM
QM deFuturo

Posts: 15
Joined: Wed Aug 05, 2009 8:40 am