prove that: log 125 = 3(1-log 2)
Answers
Answer:
Log (5^3) = Log (5^3)
Step-by-step explanation:
The question instructs that we prove that log 125 = 3 (1 - log 2)
So we will start with the right hand side of the equation, which is
3( 1- log 2)
In order to work this out, we will need to know that 1 = log 10 base 10.
We are going to substitute the 1 with log 10 base 10, hence
= 3( log 10 base 10 - log 2)
In logarithms, when a preceding a log is always its power, in that,
The 3 that precedes the logarithms in the brackets is the power of the logs, so we are going to take the 3 and say,
( Log 10 base 10 - log 2)^3
In logarithms also, the difference between two logarithmic numbers is solved by dividing them, in that:
Log m - log n = Log ( m ÷ n)
Since we have two logarithms within the brackets, we'll use this law
Log (10 ÷ 2) , which gives us Log (5^3 )
So we have,
Log 125 = Log (5^3)
When we move to the left hand side, we have, Log 125
We now have to break down the 125 to its cube root power and we will have, 125 = 5^3
In full, the resulting equation becomes,
Log (5^3) = Log ( 5^3) , which proves that they are equal.