Question

Solve:

Answer 1

\[10^{\log_{p}(\log_{q}(\log_{r}x)} = 1\]and
\[\log_{q}(\log_{r}(\log_{p}x))=0\]

Then p equals to -
a)r^{q/r} c)1
b)rq d)r^{r/q}

Answer 2

@Callisto @ganeshie8

Answer 3

its A

Answer 4

\[\log_b1=0\]

Answer 5

@nitz its A .How?

Answer 6

\[ 10^{\log_p (\log_q (\log_r x) ) } = 1\]
\[ \log_p (\log_q (\log_r x) ) = 0\]
\[ p^0 = \log_q (\log_r x)\]
\[ \log_q (\log_r x) = 1\]
\[q = \log_r x\]
\[r^q = x\]
then
\[\log_q (\log_r (\log_p x) ) = 0\]
\[q^0 = \log_r (\log_p x)\]
\[\log_r (\log_p x) = 1\]
\[r = \log_ p x\]
\[p^r = x\]
since both equations are equal to x i can equate them to one another
\[p^r = r^q\]
so i want p so i raise both sides to 1/r
\[p = (r^q)^{1/r}\]
\[p = r^{q/r}\]
got it?

Answer 7

so yes it's A nitz was right

Answer 8

just tell me if something wasnt clear for you ^_^

Answer 9

got it.

Answer 10

great stuff @lgbasallote
\[\log_bb=1\]