the laws of logs

In your next 109 workshop (workshop 5) you will see that an exponential equation (that describes an exponential graph) has been converted to a straight line equation by using logarithms. It is going to be useful for you to be able to do this conversion yourselves - and I will go through this in my next post - but before I do that I want to make sure you are ok with how to manipulate logarithms...

Here are some of the laws of logarithms:

1. Log₁₀ (m x n)    =    Log₁₀m + Log₁₀n

proof:

Log₁₀ (100 x 100)  =  Log₁₀ (10000) =   4

which is the same as:

Log₁₀ (100 x 100)  =  Log₁₀100  +  Log₁₀100  =   2 + 2  =   4

2. Log₁₀ (m / n)    =    Log₁₀m - Log₁₀n

proof:

Log₁₀ (1000 / 100)    =    Log₁₀10  =  1

which is the same as:

Log₁₀ (1000 / 100)    =    Log₁₀1000 - Log₁₀100  =  3 - 2  =  1 

3. Log₁₀ (mⁿ)    =    n x Log₁₀m 

proof:

Log₁₀ (100²)  =  Log₁₀ (10000) =   4

which is the same as:

Log₁₀ (100²)  =  2 x  Log₁₀100  =   2 x 2  =   4

It is going to be useful for you to be familiar with these rules for 109 workshop 5...