Please Help!! - Logarithims

Question

If log_x2.5=p and log_x5=q, find expressions in the terms of p and q for

a) log_x2.5

b) log₂5

Thank you so much for your help!!

Answer 1

log_x2.5 = log_x(5/2) = log_x5 - log_x2 = q - log_x2 = p

So, log_x2 = q - p

Using the change of base formula (converting from base 2 to base x), we have:

log₂5 = (log_x5) / (log_x2) = q / (q - p)

For part a, the answer is given???

Answer 2

This is the most fundamental aspect of logarithms which you need to understand ; that is the ability to go from log to exponential form and visa versa

logx 2.5 = p is tasking what power do you need to raise x to to get 2.5. Well that by definition of logs is p

so this is equivalent to x^p= 2.5