Question

(07.03)

Write log3 6 as a logarithm of base 2. (1 point)


log base 2 of 3 over log base 2 of 6
log base 2 of 6 over log base 2 of 3
log base 3 of 2 over log base 6 of 2
log base 6 of 2 over log base 3 of 2

Answer 1

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

Answer 2

Log base 2 of 6 over log base 2 of 3

Explanation:

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

`log_(a)b = (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 = (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