Evaluate (log2 27)/(log2 3)

Answer 1

Using the change of base formula for logarithms, we can write:

log2 27 = log 27 / log 2
log2 3 = log 3 / log 2

So the expression becomes:

(log 27 / log 2) / (log 3 / log 2)

We can simplify this by multiplying the numerator and denominator by log 2:

log 27 / log 3

Now we use the fact that log a / log b = logb a, so:

log3 27

Since 3^3 = 27, we have:

log3 27 = 3

Therefore, the original expression simplifies to 3.

So:

(log2 27)/(log2 3) = 3