PLEASE HELP!! :(:(:(:(
Favorites|Homepage
Subscriptions | sitemap
HOME > > PLEASE HELP!! :(:(:(:(

PLEASE HELP!! :(:(:(:(

[From: ] [author: ] [Date: 11-12-12] [Hit: ]
in what follows, will begin by changing the base 27 logarithm to a base 3 logarithm.More, precisely, how do we turn log(base 27) X into a log(base 3) quantity?There is quite a simple formula for changing a log(base A) formula to a formula involving log(base B),......
Im freaking out because I have a test tomorrow and I dont know how to do this question please help me :(

4log (base 3) X +9log (base 27) X = 14


PLEASE PLEASE PLEASE

-
Whenever I run into a problem involving logarithms of different bases, I tell myself to do one thing: MAKE THEM THE SAME BASE.

It doesn't matter which one you do, you can either change the base 3 logarithm to base 27, or you could change the base 27 logarithm into a base 3 logarithm. I, in what follows, will begin by changing the base 27 logarithm to a base 3 logarithm.

More, precisely, how do we turn log(base 27) X into a log(base 3) quantity? There is quite a simple formula for changing a log(base A) formula to a formula involving log(base B), here it is:

log(base A) X = (log(base B) X ) / (log (base B) A)

So, applying to the specific problem, we see:

log(base 27) X = (log(base 3) X) / (log(base 3) 27)

Now, log(base 3) 27 = K, where K is some number, implies that 3 to the power of K is equal to 27. Thus, the value of K is 3, since 3 to the power of 3 is 27. This can be substituted into the above:

log(base 27) X = (log(base 3) X) / 3 = (1/3) log (base 3)X

So, our new Left Hand Side of the original equation is, after changing the base of the second logarithm term:

4 log (base 3) X + 9 ((1/3) log (base 3) X) = 4 log (base 3)X +3 log (base 3) X

= 7 log (base 3) X

Substituting this into the original equation:

7 log (base 3) X = 14

This implies, dividing the 7 on both sides: log (base 3) X = 2

Remembering what a logarithm actually is, we remember that log(base A)B = k implies that A^k = B.
Similarly, the above logarithm implies that 3(the base) raised to the power of 2 (the logarithm value) is equal to X.

X = 3^2 = 9

Hope that helps!!

-
4log(base3) X + 9log(base27) X = 14

4log(base3) X + 9log(base3) X / log(base3) 27 = 14

4log(base3) X + 9log(base3) X / 3 = 14

4log(base3) X + 3log(base3) X = 14

log(base3) X^4 + log(base3) X^3 = 14

log(base3) (X^4 * X^3) = 14

log(base3) X^7 = 14

3^14 = X^7

(3^2)^7 = X^7

9^7 = X^7

X = 9 <----answer
1
keywords: HELP,PLEASE,PLEASE HELP!! :(:(:(:(
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .