Never understood logs. Please help?

Question

Evaluate the expression log 8 1.

1

None of these

0

0.9

8

Answer 1

What's to understand?  They're just tree trunks.

Answer 2

Before understanding logs, you have to understand powers. As an example, 8 to the power of 2 (this is the same as 8x8, or 8 squared) is 64. Then 8 to the power of 3 (this is the same as 8x8x8, or 8 cubed) is 512. Each time the power goes up by 1, the previous value gets multiplied by 8

Working backwards:

8 to the power of 2 is the same as (8 to the power of  3) divided by 8.

8 to the power of  1 is the same as (8 to the power of 2) divided by 8. Surprise, surprise, 8 to the power of 1 equals 8, and indeed a to the power of 1 equals a, whatever the value of a

8 to the power of 0  is the same as (8 to the power of 1) divided by 8.

Of course, a power does not have to be a whole number. 8 to the power of 1/2 has a value somewhere in between 8 to the power of 0 and 8 to the power of 1. It is in fact the same as the square root of 8, which is not a whole number either.

Now logarithms are like powers. Saying that 8 to the power of 2 equals 64 is the same as saying that the logarithm of 64 is 2, if the base is 8. Again, if the base is 8 then the logarithm of 512 is 3. (If the base is 10, then the logarithm of 1000 is also 3)

You are being asked to evaluate the logarithm (to the base 8) of 1. You should not need any more clues, but I can tell you that the correct answer is not "None of these".

Answer 3

Tree trunks or things that float in your toilet