Logarithm question

Printable View

March 30th 2009, 05:49 AM
siddscool19

Logarithm question

If x,y,z>0, $xy\neq1, yz\neq1, zx\neq1$ and $xyz\neq1, then \frac{1}{\log_{xy}(xyz)}$ $+\frac{1}{\log_{yz}(xyz)}+\frac{1}{\log_{zx}(xyz)} =$

a)1

b)2

c)3

d)4

I am new to logarithm. I know only the basics. Can anyone tell me from where I can learn logarithm in detail. Thanks in advance.

This question is from the sample paper of my entrance exam I need to learn algorithm to this level so that I can get clear. :)
I hope someone can help :). Thanks once more time in advance.
March 30th 2009, 05:52 AM
NonCommAlg

Quote:

Originally Posted by siddscool19

If x,y,z>0, $xy\neq1, yz\neq1, zx\neq1$ and $xyz\neq1, then \frac{1}{\log_{xy}(xyz)}$ $+\frac{1}{\log_{yz}(xyz)}+\frac{1}{\log_{zx}(xyz)} =$

a)1

b)2

c)3

d)4

I am new to logarithm. I know only the basics. Can anyone tell me from where I can learn logarithm in detail. Thanks in advance.

This question is from the sample paper of my entrance exam I need to learn algorithm to this level so that I can get clear. :)
I hope someone can help :). Thanks once more time in advance.

Hint: b) is the answer.
March 30th 2009, 08:56 AM
Soroban

Hello, siddscool19!

Quote:

If $x,y,z\,>\,0,\;xy\neq1,\:yz\neq1,\:xz\neq1,\:xyz\ne q1,$

then: . $\frac{1}{\log_{xy}(xyz)} + \frac{1}{\log_{yz}(xyz)}+\frac{1}{\log_{zx}(xyz)}$ equals:

. . $(a)\;1 \qquad (b)\;2 \qquad (c)\;3\qquad (d)\;4$

We're expected to know this identity: . $\log_a(b) \:=\:\frac{1}{\log_b(a)}$

Then: . $\frac{1}{\log_{xy}(xyz)} \;+\; \frac{1}{\log_{yz}(xyz)} \;+\; \frac{1}{\log_{zx}(xyz)} \;\;=\;\;\log_{xyz}(xy) \;+\; \log_{xyz}(yz) \;+\; \log_{xyz}(zx)$

. . . $= \;\;\log_{xyz}(xy\cdot yz \cdot zx) \;\;=\; \;\log_{xyz}(x^2y^2z^2) \;\;=\;\;\log_{xyz}(xyz)^2$

. . . $= \;\;2\cdot\underbrace{\log_{xyz}(xyz) }_{\text{This is 1}}\;\;= \;\;2 \quad\hdots\;\;{\color{blue}\text{answer (b)}}$
March 31st 2009, 08:32 AM
stapel

Quote:

Originally Posted by siddscool19

I am new to logarithm. I know only the basics. Can anyone tell me from where I can learn logarithm in detail.

To learn about logs, try the following:

. . . . .Google results for "logarithms introduction"
. . . . .Google results for "log rules"
. . . . .Google results for "graphing logarithmic functions"
. . . . .Google results for "solving logarithmic equations"
. . . . .Google results for "logarithmic word problems"

Have fun! :D