LOGARITHMS
What is Logarithm?
A logarithm is the power to which a number must be raised in order to get some other number.
For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100:
log 100 = 2
because,
102 = 100
Properties for Condensing Logarithms
Property 1: 0=loga 1= Zero-Exponent Rule
Property 2: 1 = loga a
Property 3: loga x + loga y loga (xy) – Product Rule
Property 4: loga x – loga y = loga (x/y) – Quantient Rule
Property 5: y loga x = loga x3 – Power Rule
What is Exponent in Logarithms?
An exponent refers to the number of times a number is multiplied by itself.
For example, 2 to the 3rd (written like this: 23) means:
2 x 2 x 2 = 8.
23 is not the same as 2 x 3 = 6.
*Remember that a number raised to the power of 1 is itself*.
For example:
a1 = a
51 = 5
There are some special cases:
Question 1. a0 = 1
(When an exponent is zero, as in 60, the expression is always equal to 1).
a0 = 1
60 = 1
14,3560 = 1
Question 2. a-m = 1 / am
(When an exponent is a negative number, the result is always a fraction. Fractions consist of a numerator over a denominator. In this instance, the numerator is always 1. To find the denominator, pretend that the negative exponent is positive, and raise the number to that power, like this):
a-m = 1 / am
6-3 = 1 / 63
(You can have a variable to a given power, such as a3, which would mean a x a x a. You can also have a number to a variable power, such as 2m, which would mean 2 multiplied by itself m times. We will deal with that in a little while).
Example of Logarithm
Example Question 1: Solve log3 (9x+2) = 4
Log3 (9x+2) = 4
9x + 2 = 34
9x + 2 =81
X= 79/9
Final Answer: log3 (9x+2) = 4 is x=79/9
Example Question 2: Write in exponential form: log232 = 5.
Final Answer: 25 = 32.
| Example Question 3: Write in logarithmic form: 4−2 = | 1 16 | . |
| Final Answer: log4 | 1 16 | = −2. |
Here the questions for you to solve:
1. Question: Evaluate log81
2. Question: Evaluate log55
Have a nice day :)
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