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

Answer:

$log_{x}$45 = 2p + q

Step-by-step 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