Since a logarithm is simply an exponent which is just being written down on the line, we expect the logarithm laws to work the same as the rules for exponents.

Slide 3:

Exponents Logarithms
bm × bn = bm+n logb xy = logb x + logb y
bm ÷ bn = bm-n logb (x/y) = logb x − logb y
(bm)n = bmn logb (xn) = n logb x
b1 = b logb (b) = 1
b0 = 1 logb (1) = 0

Slide 4:

Note: On our calculators, "log" (without any base) is taken to mean "log base 10". So, for example "log 7" means "log107".

1. Expand log 7x as the sum of 2 logarithms. :

1. Expand log 7x as the sum of 2 logarithms. Sol: Using the first law given above, our answer is
log 7x = log 7 + log x
Note: This has the same meaning as 107 × 10x = 107+ x

2. Using your calculator, show thatlog (20/5) = log 20 − log 5. :

2. Using your calculator, show thatlog (20/5) = log 20 − log 5. using numbers this time so you can convince yourself that the log law works.
LHS
= log (20/5)
= log 4
= 0.60206 (using calculator)
Now,

Slide 7:

RHS
= log 20 − log 5
= 1.30103 − 0.69897 (using calculator)
= 0.60206
= LHS
We have shown that the second logaritm law above works for our number example.

3. Express as a multiple of logarithms: log x5. :

3. Express as a multiple of logarithms: log x5. Using the third logarithm law, we have
log x5 = 5 log x
We have expressed it as a multiple of logarithm, and it no longer involves an exponent.

Slide 9:

Note 1: Each of the following is equal to 1:
log6 6 = log10 10 = logx x = loga a = 1
The equivalent statements, using ordinary exponents, are as follows:
61 = 6
101 = 10
x1 = x
a1 = a

Slide 10:

Note 2: All of these are equivalent to 0:
log7 1 = log10 1 = loge1 = logx 1 = 0
The equivalent statments in exponential form are:
70 = 1
100 = 1
e0 = 1
x0 = 1

THANK YOU :

THANK YOU

You do not have the permission to view this presentation. In order to view it, please
contact the author of the presentation.

Send to Blogs and Networks

Processing ....

Premium member

Use HTTPs

HTTPS (Hypertext Transfer Protocol Secure) is a protocol used by Web servers to transfer and display Web content securely. Most web browsers block content or generate a “mixed content” warning when users access web pages via HTTPS that contain embedded content loaded via HTTP. To prevent users from facing this, Use HTTPS option.

By: allan4k4 (72 month(s) ago)

nice presentation....it is very useful for childrens...