Question #cab16

2 Answers
Dec 8, 2017

#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

Dec 8, 2017

#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#