Download Logarithms Logarithm is a tool for the solution of triangles, both right

Logarithms
Logarithm is a tool for the solution of triangles, both right and oblique.
A logarithm is another name for an exponent. In general, if a number N is expressed as some
power of b (b>0, b ≠ 1) by the equation.
Then the exponent x is the logarithm of the number N to the base b, that is
In this relationship, the first form is called the logarithmic form , while the second is the
exponential form.
Example
Exponential form
23 = 8
b0=1
32 -1/5 = ½
Practice exercise
Express in logarithmic form.
1. 32 = 9
2. (1/2)-5 = 8
3. ab = c
4. 64 ½ = 8
5. 64 1/3 = 4
Express in exponential form
1. log 8 64 = 2
2. log 1 = 0
3. log b m = y
4. log (9/4) (8/27) = -(3/2)
5. log 8 32 2/5 = 2/3
Solve for the value of x
1. log 2 x = 4
2. log 3 81 = x
3. log x 8 = 3
4. log 1000 = x
5. log .01 = x
Logarithmic form
log 2 8 = 3
log b 1 = 0
log 32 1/2 = -1/5
Properties of Logarithm
Property 1. The logarithm of the product of two positive numbers equals the sum of the
logarithms of the numbers.
eg.
log 6 = log 2(3) = log 2 + log 3
Property 2. The logarithm of a quotient is equal to the logarithm of the dividend minus the
logarithmic of the divisor.
eg.
log = log 8 – log 3
Property 3. The logarithm of the pth power of a number is equal to the p times the logarithm of
the number.
eg.
log 100 = log 102 = 2 log10 = 2(1) = 2
Property 4. The logarithm of the r th root a number is equal to the logarithm of a number divided
by r.
eg.
log
= log10
= (-log 1000) = (-3) = -3/2
Practice exercise
Express the following as single logarithms
1. log 5 + log 4
2. ½ log 4 + ¼ log 81
3. 2 log 3 – ½ log 9 + 3log 2
Solve for x
1. log x 4 + log x 2 = 3
2. log x 9 + log x 27 = 5
3. log x 125 + log x 5 = 2
4. log 20 + log 50 = x
5. log 50 + log 2 = x
Verify the following
1. log
- log (0.01)2 = 14/3
2. log
+ log
= -1/2
3. log 100 – log
=4