How do you evaluate log466?

1 Answer
Jun 12, 2016

x=log66log4

Using a calculator gives x=3.022

Explanation:

The answer is not going to be an integer. The question is asking:
"To what power must 4 be raised, to equal 66?"

The powers of 4 are : 4, 16, 64, 256 ....
66 is not one of them, but we can see that the required index will be 3. .....
log from is interchangeable with index form:

If log466=x then 4x=66

Let's use the index form and find the log of both sides, because the variable is in the index.
log4x=log66

xlog4=log66

x=log66log4

Using a calculator gives x=3.022

This same result could be found from the change of base law:

logab=log10blog10a

Some calculators can work with any base, but for those that only use base 10, this works fine.1