Pre-calc w-up 4/10-11

1. Write the equation loge 13.7 = x in exponential form

2. Write the equation (1/4)-4 = 256 in log form

3. Evaluate the expression log443

4. Solve log2x + log210 = log270

11.5 Common Logarithms

A common logarithm is a logarithm with a base of 10. log10x = logx

Use your properties of logarithms to simplify. Remember a logarithm is an exponent.

Ex 1: Given log8 = 0.9031 evaluate A) log 800,000

= log (100,000 x 8)

= log 105 + log 8

= 5 + 0.9031

= 5.9031

The antilog… The inverse of a logarithm is a _______ So if log x = a then ________ What… Log 11.5=_________ Antilog 1.06069784 = _____________

Try these 2a) log 54.1 2b) antilog1.9484 Answers 1.7332 88.7973

exponent

10a = x

1.06069784 – push the buttons on your calc

11.5 on calc push

2nd log 10^1.06069784 (inverse of log)

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

loglog

logb

ab

nn

a

log1043 use your calc 3.16

log9

Use logs to solve exponential functions..Ex4: solve 63x = 81Take 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 = .8175 (divided both sides by 3)

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 = x2 + 25 NODivide by a log 1st, (doesn’t matter which one) then

follow rules of solving.

log34 ( 2) now distribute

log12x x

4 ( 2).4421x x

4 .4421 .8842x x x = 5.58

Ex6: graph y= 3log(x+1)

What is the basic shape of a logarithm?Type it into your calc y = logxHow does that compare to y = 10^x?

Plug into your calculator, adjust window, label at least 3 points.

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 all19-23 NO CALC28-rest you can use a calculator