why does log296-log23=5?

Question

log₂96-log₂3=5

Answer 1

One of the rules of logarithms is:

log_b(m/n) = log_b(m) - log_b(n)

(the log of the division of two numbers equals the subtraction of their individual logs)

So log₂96 - log₂3 = log₂(96/3) = log₂(32)

Then, the conversion of logarithms to exponential is like this:

log_b(m) = n means bⁿ = m so log₂(32) means that 2^x = 32

(the logarithm IS the exponent)

That means x must be 5 since 2⁵ = 32 (5 is the exponent that applied to the base "2" will yield 32 as the result)