1. Pre-calc w-up 4/10-11
Write the equation loge 13.7 = x in exponential form
Write the equation (1/4)-4 = 256 in log form
Evaluate the expression log443
Solve log2x + log210 = log270

2. A common logarithm is a logarithm with a base of 10. log10x = logx
11.5 Common Logarithms
A common logarithm is a logarithm with a base of 10.
log10x = logx

3. Ex 1: Given log8 = 0.9031 evaluate
Use your properties of logarithms to simplify. Remember a logarithm is an exponent.
Ex 1: Given log8 = evaluate
A) log 800,000
= log (100,000 x 8)
= log log 8 = =

4. The antilog… The inverse of a logarithm is a _______
So if log x = a then ________
What…
Log 11.5=_________
Antilog = _____________
Try these 2a) log b) antilog1.9484
Answers
exponent
10a = x
– push the buttons on your calc
11.5 on calc push
2nd log 10^ (inverse of log)

5. Change of base – we want base 10 then we can use our calculators.
a,b,n are positive and a and b don’t equal 1 then the change of base formula is…
Ex 3: find the value of log9 1043

6. Use logs to solve exponential functions..
Ex4: solve 63x = 81
Take the log of both sides
log63x = log 81
“finding answers in the hunt powers of log can go up front”
3x log 6 = log 81 (now solve)
3x = log81/log6 (divided both sides by log6)
x = (divided both sides by 3)

7. Ex 5: 12x-4 = 3x-2
Take the log of both sides, bring powers up front
(x – 4)log12 = (x – 2) log3
You can NOT distribute the log, a log is an exponent
Do you do this (x + 5)2 = x NO
Divide by a log 1st, (doesn’t matter which one) then follow rules of solving.
x = 5.58 

8. Ex6: graph y= 3log(x+1) What is the basic shape of a logarithm?
Type it into your calc y = logx
How does that compare to y = 10^x?
Plug into your calculator, adjust window, label at least 3 points.

9. Remember:
Logs in real number system are undefined for negative numbers.
You can get a negative answer, you can’t take a log of a negative number
Homework: pg 730 # 19-21,23,28 – 45 all
19-23 NO CALC
28-rest you can use a calculator