# Need a few logarithm formulas...

• 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: $\displaystyle 4^{4x}=2000; x=?$

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

...so I basically just need to know what $\displaystyle x$ equals, and just plugging in numbers isn't very practical :( Can anyone help?
• May 30th 2009, 03:38 PM
artvandalay11
$\displaystyle 4^{4x}=2000$ take the log of both sides
$\displaystyle log(4^{4x})=log(2000)$ but now, one of the log rules says that $\displaystyle log(a^b)=b*log(a)$

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

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

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

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=$\displaystyle \frac{log2000}{8log2}$ the answer? Because when I put that into a calculator, I get $\displaystyle .1242136307$, and then when I add that value into the equation

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

I get $\displaystyle 1.991297872$, which isn't close to 2,000...
• May 30th 2009, 04:03 PM
artvandalay11
$\displaystyle x=\frac{log2000}{8log2}$ when you put it in your calculator, you didn't use order of operations correctly so your calculator did this: $\displaystyle \frac{log2000}{8}*log2$
• May 30th 2009, 04:09 PM
stewardship37
Ahhhh ok. I went back and entered it in as:
Code:

(log(2000))/(8log(2))
And got $\displaystyle 1.370723036$, which worked perfectly...thanks for all of your help :)