The single logarithm term would be log(b - x)
Explanation:
Given:
(logₓ a) (logₐ b)
We have to write it in single logarithm
We have to use the formula
[tex]log_a (m) = \frac{log (m)}{log(a)} \\\\[/tex]
So, we can write (logₐ b) as [tex]\frac{log (b)}{log(a)}[/tex] and (logₓ a) as [tex]\frac{log(a)}{log(x)}[/tex]
So,
(logₓ a) (logₐ b) = [tex]\frac{log (a)}{log(x)} X \frac{log (b)}{log (a)}[/tex]
= [tex]\frac{log(b)}{log(x)}[/tex]
= log (b - x)
Therefore, the single logarithm term would be log(b - x)
