# logarithms

#### Elaine

##### New member
log 4 0.287

change the base rule to find the logarithm to four decimal places.

#### tkhunny

##### Moderator
Staff member
You can get an idea by checking the exponential form.

If log<sub>4</sub>(0.287) = 13.9373, then 4<sup>13.9373</sup> = 0.287. I think not!

Estimate first. Then you can't make that kind of error.

4<sup>1</sup> = 4
4<sup>0</sup> = 1
4<sup>-1</sup> = ¼ = 0.25

That's it. The answer should be between 0 and -1, probably closer to -1.

The rule you are told to use suggests: log<sub>4</sub>(0.287) = log(0.287)/log(4).
--------------------------------