Lecture notes Business mathematics (BMD115D)

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CHAPTER 6
LOGARITHMS AND EXPONENTS

AIM : Introduction to exponents, roots, logs.

6.1 KEY SEQUENCE

S A key sequence is the order in which we press the calculator keys to solve a sum.
S Work from left to right to get the final answer.
S Once you have pressed = the operation is complete and the calculator is ready for the
next operation.
S If you see an Error (or E) on your calculator screen, you have to clear the display before
you can go on.
S To correct an operation ( + ; - ; x ; ÷ ) sign the following steps are necessary to correct
it: * press the back arrow key = ;

* then the DEL key ;
* now you are able to press the correct operation key.
S To correct an incorrect number, press the DEL key to erase each incorrect number,
then go on.
_ CA clears everything and DEL clears the last entry.

6.2 EXPONENTS

EXAMPLE 6.1
To solve : 15 x 15 the following key strokes are necessary : 15 x 15 =
and the answer on the display is 225.
But 15 can be written as 151 where 15 is the base number and 1 is the exponent. We say 15 to
the power of 1. The expression 151 is called the power. Try the exponent function on your
calculator.
The following key stokes are necessary : 15 y x 1 =
and the answer on the display is 15.

Now 15 x 15 can be written as 151 x 151. If the bases are equal, we can add the exponents
together.

Thus 151 x 151 = 151+1 = 152. Lets test our answer on the calculator.
The following key strokes are necessary : 15 y x 2 =
and the answer on the display is 225.
This is the same answer we got when we multiplied 15 by 15.

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Let us try another example and see if our rule will always work.

EXAMPLE 6.2

To solve : 7x7x7x7
The following key strokes are necessary : 7 x 7 x 7 x 7 =
and the answer on the display is 2401.

Now 7 x 7 x 7 x 7 can be written as 71 x 71 x 71 x 71. The bases are the same, so we can add the
exponents together.

Thus 71 x 71 x 71 x 71 = 71 + 1 + 1 + 1 = 74. Lets test our answer on the calculator:
The following key strokes are necessary : 7 yx 4 =
and the answer now on the display is 2401.

This is the same answer we got when we multiplied 7 by 7 by 7 by 7.

EXAMPLE 6.3

To solve : 7x9
the following key stokes are necessary : 7 x 9 =
and the answer on the display is 63.

Now 7 x 9 can be written as 71 x 91. The bases ( the “7” and the “9” ) are not equal. We can not
add the exponents together and the only way to solve the problem is by using the method in
example 6.3.



If the bases are the same then we can add the exponents together.

EXERCISE 6.1

Try the following EXERCISES yourself : Answer

6.1.1 58 x 42 º 58 x 42 = (2436)

6.1.2 10 x 103 º 10 x 10 y x 3 = (10000)
4 4
6.1.3 4 + 2 (272)

6.1.4 25 - 52 (7)

6.1. 5 3 x 3 x 3 x 4 x 4 (432)