CAT Question - Logarithms

This is a reasonably tough question. But since the messrs conducting CAT seem to have upped the ante on Logarithm, this is probably par for the course

Question

log₅x = a (This should be read as log X to the base 5 equals a)log₂₀x = b
What is log_x10 ?

Correct Answer: (a + b)/2ab

Explanation

log₅x = a
log₂₀x = b
log_x5 = 1/a
log_x20 = 1/b
log_x100/5 = 1/b
log_x100 – logn5 = 1/b
2log_x10 – 1/a = 1/b
log_x10 = ½(1/a + 1/b)
log_x10 = (a + b)/2ab