Question

question is as below

Answer 1

if p>1, q>1 and r>, then \[^{p}\log \sqrt[3]{r}^{q}\log p ^{6} \log \sqrt{q}\] is??

Answer 2

Is the first p multiplied with the whole term?

Answer 3

yess but to reconfirm i will pot the pic here

Answer 4

Sorry, I did not understand the question. Why is that p,q and r written in the superscript before log. I am confused!

Answer 5

use the change of base formula

Answer 6

i cant understand??

Answer 7

http://www.mathwords.com/c/change_of_base_formula.htm

Answer 8

i should change to base 10 is it??

Answer 9

yes

Answer 10

sorry i am clueless @ganeshie8

Answer 11

\[\large \log_p \sqrt[3]{r} . \log_q p^6 . \log_r \sqrt{q}\]

Answer 12

the given expression is like that right ?

Answer 13

@ganeshie8 Hey, but I thought that p was written in the superscript before log..can we take it in base the way you've done it?

Answer 14

it seems the printing machine has some problem with subscripts...

Answer 15

I don't know. I was confused about that thing only!

Answer 16

\[\large \log_p \sqrt[3]{r} . \log_q p^6 . \log_r \sqrt{q}\]

\[\large = \dfrac{\log \sqrt[3]{r}}{\log p } . \dfrac{\log p^6}{\log q} . \dfrac{\log \sqrt{q}}{\log r}\]

Answer 17

use log identities and cancel whatever you can

Answer 18

will i get \[\log \sqrt{r} \times \log p ^{5} \times \log q\]

Answer 19

no, you need to use below identity :
\(\large \log a^m = m \log a\)

Answer 20

\[\large = \dfrac{\log \sqrt[3]{r}}{\log p } . \dfrac{\log p^6}{\log q} . \dfrac{\log \sqrt{q}}{\log r} \]


\[\large = \dfrac{\frac{1}{3}\log r}{\log p } . \dfrac{6\log p}{\log q} . \dfrac{\frac{1}{2}\log q}{\log r} \]

Answer 21

cancel now

Answer 22

1/3 x 6 x 1/2