Question

given that logax^2y=p and that loga(x/y^2)=q find logax and logay in terms of p and q and hence express logaxy in terms of p and q

Answer 1

\[\log_{a} x^2y=p\]
\[\log_{a} (x/y^2)=q\]
\[\log_{a} x^2y=\log_{a} b^p\]
\[x^2y=a^p\]
\[\log_{a} (x/y^2)=\log_{a} a^q\]
\[x/y^2=a^q\]

Answer 2

@ganeshie8 i dont know how the answers are
\[\log_{a} x=1/5(2p+q)\]
\[\log_{a} y=1/5(p-2q)\]
\[\log_{a} xy=3/5p-1/5q\]
so do you have any idea on figuring out this question

Answer 3

we're given these :
\(\large \log_a \left( x^2y\right) = p\)

\(\large \log_a \left(\frac{x}{y^2}\right) = q\)

Answer 4

yes

Answer 5

\(\large \log_a \left( x^2y\right) = p \\ \large \implies \log_a x^2 + \log_a y = p \\ \large \implies 2\log_a x + \log_a y = p ~~~~\color{red}{(1)}\)

Answer 6

\(\large \log_a \left( \frac{x}{y^2}\right) = q \\ \large \implies \log_a x - \log_a y^2 = q \\ \large \implies \log_a x - 2\log_a y = q ~~~~\color{red}{(2)}\)

Answer 7

solve \(\large \color{red}{(1)}\) and \(\large \color{red}{(2)}\)

Answer 8

why in the 2nd equation is it logay^2

Answer 9

is this a rule to log both sides of the fraction

Answer 10

yes here are the rules :

\(\large \log_a \left(M*N\right) = \log_a M + \log_a N\)


\(\large \log_a \left(\frac{M}{N}\right) = \log_a M - \log_a N\)

Answer 11

oh i forgot that rule thank you so much
\[5\log_{a} x=2p+q\]
\[2p+q/5=\log_{a} x\]
\[2*(2p+q/5)+\log_{a} y=p\]
\[\log_{a} y=-2q+p/5\]
\[\log_{a}xy= \log_{a}x+\log_{a} y\]
\[(2p+q/5)-(p-2q)/5\]