Question

How do you find the value of `log_7 4` using the change of base formula?

Answer 1

`0.715`

Explanation:

You can use the change of base formula to be able to use `log_10`

`log_7 4 = (log_10 4)/(log_10 7)`

This is now calculated with a calculator:

`=0.715`

The follow explains where the rule comes from...

`log_7 4 = x " "hArr" " 7^x = 4" larr` log both sides

`color(white)(xxxxxxxxxxxxxx)log7^x = log 4" "larr` power law

`color(white)(xxxxxxxxxx.xxx)xlog7 = log 4" "larr` isolate x

`color(white)(xxxxxxxxxxxxxxxxx)x = log4/log7`