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Answer 1 · 2017-12-08T17:01:05

$x~~0.78$

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 · 2017-12-08T17:06:45

$log(6)~=0.778$

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:
$log(3*2)=log(3)+log(2)~=0.301+0.477=0.778$