Question

(07.03)

Answer 1

The answer would be log base 2 of 6 over log base 2 of 3

Answer 2

Answer:

Log base 2 of 6 over log base 2 of 3

Step-by-step explanation:

In order to make a change of base of a logarithm, we apply this principle:

$log_{a}b = \frac{log_{c}b}{log_{c}a}$

Where:

a: current base of the logarithm [in this case a = 3]

b: argument of the logarithm [in this case b = 6]

c: new base of the logarithm [in this case c = 2]

Applying this principle in this exercise, we have:

$log_{3}6 = \frac{log_{2}6}{log_{2}3}$

This quotient of logarithms can be expressed as:

Log base 2 of 3 over log base 2 of 6