# Thread: Logarithm question

1. ## Logarithm question

If x,y,z>0,$\displaystyle xy\neq1, yz\neq1, zx\neq1$ and $\displaystyle xyz\neq1, then \frac{1}{\log_{xy}(xyz)}$$\displaystyle +\frac{1}{\log_{yz}(xyz)}+\frac{1}{\log_{zx}(xyz)} = a)1 b)2 c)3 d)4 I am new to logarithm. I know only the basics. Can anyone tell me from where I can learn logarithm in detail. Thanks in advance. This question is from the sample paper of my entrance exam I need to learn algorithm to this level so that I can get clear. I hope someone can help . Thanks once more time in advance. 2. Originally Posted by siddscool19 If x,y,z>0,\displaystyle xy\neq1, yz\neq1, zx\neq1 and \displaystyle xyz\neq1, then \frac{1}{\log_{xy}(xyz)}$$\displaystyle +\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.

3. Hello, siddscool19!

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

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

. . $\displaystyle (a)\;1 \qquad (b)\;2 \qquad (c)\;3\qquad (d)\;4$
We're expected to know this identity: .$\displaystyle \log_a(b) \:=\:\frac{1}{\log_b(a)}$

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

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

. . . $\displaystyle = \;\;2\cdot\underbrace{\log_{xyz}(xyz) }_{\text{This is 1}}\;\;= \;\;2 \quad\hdots\;\;{\color{blue}\text{answer (b)}}$

4. 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!