Log, find the following values in term of m and n

Question

I have a hard time on this log question, can you explain it?

Given log(x)p = m and log(x)q = n find the following values in termm of m and n:

1) log(x)p^3q

2) log(x)P/q^2

the base are (x)

For the first one my attempt are

(log(x)m^3 )( log(x)n) = nm^3

the second one i have no idea how to do it

thanks guys

Answer 1

Assuming that by log(x)p you mean ${\log_x}{p}$ and that by log(x)P/q^2 you mean ${\log_x}{p/q^2}$ then you would proceed as follows...

1) ${\log_x}{p^{3}{q}} = 3\log_x{p} + \log_xq = 3m + n$

2) $\log_x{p/{q^2}} = \log_x{p} - 2\log_x{q} = m - 2n$

Note that to simplify I used the rules...

1) $\log(ab) = \log{a}+\log{b}$ and

2) $\log{a^c} = c\log{a}$