# The Logarithm Laws

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Category: Education

## Presentation Description

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By: allan4k4 (67 month(s) ago)

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

## Presentation Transcript

### The Logarithm Laws :

The Logarithm Laws

### Slide 2:

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

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