Question

How do you calculate `log_4 28`?

Answer 1

`log_4 28=2.4037`

Explanation:

Using the identity `log_b a=(log_n a)/(log_n b)`, if we choose `n=10`, then

`log_4 28=log28/log4`

Now using tables as `log28=1.44716` and `log4=0.60206`

`log_4 28=1.44716/0.60206=2.4037`

Answer 2

`2.404`

Explanation:

Log form and index form are interchangeable, and sometimes one form is easier to use than the other.

Note that: `log_a b = c" "harr" " a^c = b`

"The base stays the base and the other two change around"

`log_4 28 = x" "harr " " 4^x= 28`

We can see that this is not an integer answer because:

`4^2 = 16 and 4^3 = 64` x is between 2 and 3.

`4^x= 28 " log each side"`

`xlog 4 = log 28" power law as well"`

`x = (log28)/(log4)" isolate x"`

`x = 2.404" calculator or tables"`

The same result would have been obtained using
the change of base law.