Question

How do I rewrite the following as a single logarithmic expression?

3log(b)m-2log(b)n
thank you!

Answer 1

The expression is
`3\log_bm-2\log_bn`.

Recall the following rules:

i)
`\displaystyle{ \log_ba-\log_bc=\log_b{(a)/(c)}`

ii)
`\displaystyle{ a\log_bc= \log_bc^a`


First, by the rule (ii) we have:


`3\log_bm-2\log_bn=\log_bm^3-\log_bn^2.`

Second, by rule (i), we have:


`\displaystyle{ \log_bm^3-\log_bn^2=\log_b{(m^3)/(n^2)}.`


Thus, the answer is :
`\displaystyle{ \log_b{(m^3)/(n^2)}`