Question

given that log base x 3=p and log base x 5=q, express the following in terms of p and q: log base x 45

Answer 1

`log_(x)`45 = 2p + q

Explanation:

using the laws of logarithms

• log x + log y = log(xy)

• log
`x^(n)` ⇔ nlogx

`log_(x)`45 =
`log_(x)`(3² × 5 )

= log 3² + log 5 ( to base x )

= 2log 3 + log 5 ( to base x )

= 2p + q