Need a few logarithm formulas...

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May 30th 2009, 03:05 PM
stewardship37

Need a few logarithm formulas...

Or at least I think I do...

These are the two problems I have:

#1: $4^{4x}=2000; x=?$

#2: $4log(x-4)=16; x=?$

...so I basically just need to know what $x$ equals, and just plugging in numbers isn't very practical :( Can anyone help?
May 30th 2009, 03:38 PM
artvandalay11

$4^{4x}=2000$ take the log of both sides
$log(4^{4x})=log(2000)$ but now, one of the log rules says that $log(a^b)=b*log(a)$

so $4x*log4=log2000$ and $4x=\frac{log2000}{log4}$ so just divide by 4 and x= $\frac{log2000}{4log4}$

in general though, people seem to like to reduce logs for no reason that I can see... so log4= $log2^2=2log2$ so x= $\frac{log2000}{8log2}$

$4log(x-4)=16$ divide by 4 and log(x-4)=4, now raise each side to a power of 10, so $10^{log(x-4)}=10^4$

so x-4=10000, and x=10004
May 30th 2009, 04:00 PM
stewardship37

Thanks man, I understand the second one, but for the first one, is x= $\frac{log2000}{8log2}$ the answer? Because when I put that into a calculator, I get $.1242136307$ , and then when I add that value into the equation

$4^{4x}=2000$ as $4^{4 * .1242136307}$

I get $1.991297872$ , which isn't close to 2,000...
May 30th 2009, 04:03 PM
artvandalay11

$x=\frac{log2000}{8log2}$ when you put it in your calculator, you didn't use order of operations correctly so your calculator did this: $\frac{log2000}{8}*log2$
May 30th 2009, 04:09 PM
stewardship37

Ahhhh ok. I went back and entered it in as:

Code:

(log(2000))/(8log(2))

And got $1.370723036$ , which worked perfectly...thanks for all of your help :)