Condense the following

Question

2(log2 5 +log2 p)-1/2log2 36

Answer 1

You can only condense logarithms when they all have the same base. For our problem they all have a base of 2 so we can condense to a single logarithm.

2(log₂ 5 + log₂ p) - 1/2(log₂ 36)

log₂ 5² + log₂ p² - log₂ 36^1/2 coefficients in front of logarithms are powers to the argument of the logarithms

log₂ 5²(p²) - log₂ 6 logarithms added together are combined to one and you multiply the arguments

log₂ (5²p² / 6) the difference of logarithms are combined to one and you divide the arguments

The answer is log₂ (25p² / 6)