Question

Question #cab16

Answer 1

`x~~0.78`

Explanation:

Ok before I begin, I would like to point out that `log 6` ACTUALLY means `log_10 6`. When the subscript is not stated, it is implied to be `10`.

Ok, so logarithms are simply the inverse to exponentials. An easy way to ALWAYS solve logarithms easily is just remember this simple rule.

`log_a b = c` is the same as `b = a^c`

Heres an example:

`log_2 64 = 6` OR `64 = 2^6`

So for your question, the answer is

`log_10 6 = ?` OR `6=10^?`

Honestly this is a very difficult problem to solve without a calculator. My calculator says that `x~~0.78`

I hope that answers your question regarding logarithms!
~Chandler Dowd

Answer 2

`log(6)~=0.778`

Explanation:

Logarithms can be thought of as the reverse of exponents. The expression `log_b(x)=y` is the same as solving the following equation for `y`:

`b^y=x`

So `log(6)` can be thought of "what number do I have to raise `10` to to get `6`?" (`log` is usually shorthand for `log_10`).

In this case, we only have the values of the logarithms provided, so we're going to take advantage of the fact that `6` can be written as `3*2`

`log(6)=log(3*2)`

Then I'm going to take advantage of the following logarithm property:
`log_x(a*b)=log_x(a)+log_x(b)`

So our logarithm becomes:
`log(3*2)=log(3)+log(2)~=0.301+0.477=0.778`