Use properties of logarithms to show that log(3) + log(4) + log(5) − log(6) = 1
Mathematics · High School · Thu Feb 04 2021
Answered on
We know that the property of log is
Log (m ) + log(n ) = log (m*n) ……(1)
Log (m) - log (n)= log (m/n) ………(2)
Given equation
Log(3)+log(4)+log(5)-log(6)=1
By using the equation (1)
Log(3*4)+log(5) -log(6)=1
Log(12)+log(5)-log(6)=1
Again using equation (1)
Log(12*5)-log(6)=1
Log(60)-log(6)=1
By using equation (2)
Log (60/6)=1
Log(10)=1
We know that the value of log (10) =1
So 1=1 proof.