Applications of Log Rules

We are just substituting in for each expression!

What happened to the log 1?

To determine what happens to the log 1, we need to rewrite it in exponential form! b to what power = 1? Therefore, x=0. This brings up an important result, log 1 = 0! Any base the zero power is one (except 0).

We are now going to do the same type of problems with powers of 10. Remember that your computer can do base 10. We need to keep the expression equal to 4.6. By rewriting it as 460/100, we can now use the log rules and substitute what we know! Log 460 is equal to b Log 100 is equal to 2, use calculator

We need to keep the expression equal to By rewriting it as 3.15*1000, we can now use the log rules and substitute what we know!

Some random log rules: 1. We can not take the log of zero (0) or a negative. For what values of x is the expression defined? Since we can not take the log of 0 or a negative, we write an inequality to solve for x. Thus, x is defined for all values of x > 2. For what values of x is the expression UNDEFINED? Thus, x is undefined for all values of x less than or equal to -3/2.

Some random log rules: 2. The log of one is always zero. log 1 = 0 I will now rewrite it exponentially to show you why! Anything (except 0) raised to the zero power is The inverse of an exponential function is a log function! Exponential function Log function Remember, when taking an inverse, it is the same as reflecting over the line y=x. You switch x & y for both!

Homework Page 5 #1,3,4,5 Page 6 #11 Page 7 #6,8,11a,c,12,a,c