### 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

Question

log

_{5}x = a (This should be read as log X to the base 5 equals a)log

_{20}x = b

What is log

_{x}10 ?

Correct Answer: (a + b)/2ab

Explanation

log

_{5}x = a

log

_{20}x = b

log

_{x}5 = 1/a

log

_{x}20 = 1/b

log

_{x}100/5 = 1/b

log

_{x}100 – logn5 = 1/b

2log

_{x}10 – 1/a = 1/b

log

_{x}10 = ½(1/a + 1/b)

log

_{x}10 = (a + b)/2ab

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