Question

expand
logp2q3 \div r4
​

Answer 1

Answer:

Given:

\log \dfrac{p^2q^3}{r}logrp2q3

We have to expand the value of \log \dfrac{p^2q^3}{r}logrp2q3is:

Solution:

∴ \log \dfrac{p^2q^3}{r}logrp2q3

Using the logarithm identity:

\log \dfrac{a}{b}logba = \log aloga - \log blogb

= \log (p^2q^3)-\log rlog(p2q3)−logr

Using the logarithm identity:

\log ablogab = \log aloga + \log blogb

= \log p^2+\log q^3-\log rlogp2+logq3−logr

Using the logarithm identity:

\log a^mlogam = m\log amloga

= 2\log p+3\log q-\log r2logp+3logq−logr

∴ The expandation of \log \dfrac{p^2q^3}{r}logrp2q3 = 2\log p+3\log q-\log r2logp+3logq−logr

Thus, the expandation of \log \dfrac{p^2q^3}{r}logrp2q3 is equal to "2\log p+3\log q-\log r2logp+3logq−logr ".