Period 1- 6.2 Logarithms

6.2 Logarithms

On Tuesday, we learned a new concept called Logarithms. Logarithms are inverse functions of x and y values are switched. Logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number. The logarithmic function is defined as y = log(b)x, or y equals the logarithm of x to the base b. The function is defined only for b > 0, B cannot equal to 1.

Ex. 1 Write in logarithmic form.

a) a^x = y

x = log(a)y

b) 2^3 = 8

3 = log(2)8

c) 5^2 = 25

2 = log(5)25

Ex. 2 Write in exponent form.

a) 3 = log(2)8

2^3 = 8

b) 2 = log(5)25

5^2 = 25

Ex. 3 Evaluating logarithms to find exact values:

a) log(2)16 = log(2)2^4 = 4

*The base and logarithm (2,2) are both cancel each other.

b) log(5)1/25 = log(5)5^-2 = -2

*1/25 is the negative inverse of exponent 2.

Law of Logarithms

LogA^b = b log a

Ex 4. Solve.

a) log(2)8^4 = 4log(2)8

= 4(3) *2 to the power of 3 = 8

= 12

b) log(3)2^5 = 5log(3)27

= 5(3) *3 to the power of 3 = 27

= 15

These are the basics laws/ways of solving for logarithms. I'm sorry for posting this a little late. Hope this post has been useful!