Hello friends, welcome here. For today, we will be sharing with the students of Form 5 some Logarithms and indices sample MCQ questions.

These sample questions should help you get familiarised with the way the Maths paper 1 MCQ is usually set.

We are sharing these questions since the GCE O/L program for Mathematics includes the Multiple Choice Questions (MCQ) which as earlier said is what you will see in all GCE Paper 1.

But before we dive into the MCQ questions, let’s first of all brief you on what Logarithms and Indices are all about.

Logarithms and indices basic concepts

Logarithms

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number X is the exponent to which another fixed number, the base b, must be raised, to produce that number.

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number Χ. ^[1]

Simply put, the log of a number X to a given base Y is the power to which we can raise the base to give the number. For example:

log₂8 = 3

From the above example, we can see that the power to which we can raise the base (2) to give the number (8) is three (3). This, therefore, makes us say that;

if y = a^x then log_ay = x

Laws of log

	Formula
Product
Quotient
Power
Root

Multiplication Law

What is the rule when you multiply two values with the same base together (x² * x³)?

The rule is that you keep the base and add the exponents. Well, remember that logarithms are exponents, and when you multiply, you’re going to add the logarithms.

Therefore, this brings us to say that, the log of the products of two numbers to a base is the sum of the logs of the individual numbers to the given based. i.e;

log_a(bc) = log_ab + log_ac

Also, it should be noted that there is no role for multiplying individuall logs to a particular base except if the two logs are in such a way that the number of the first log is the base of the second.

That is ⇔ log_ab * log_bc  is possible but log_ab * log_ac isn’t possible.

And from the above explanation, we will have;

log_ab * log_bc = log_ac

Indices

An index (plural indices) is a whole number power. That is, it is the name given to the power to which a given number (base) is raised to. So, basically, an index is an exponent.

Laws of indices

	Formula
Product	xa * xb = xa+b
Quotient	xa ÷ xb =  xa-b
Power	(xa)b = xab
Root	x1/a = a√x
Zero index	x0 = 1
Negative index	x-a = 1/xa

Logarithms and indices sample MCQ question

Now that you have refreshed your memories on what log and indices are all about, let’s see how you tackle the following MCQ questions.

SECTION A: Logarithms

1)  The value of log₅625 is

A: 25

B: 5

C: 4

D: 3

2)  y = 3^x when written in log form is?

A: log_yx = 3

B: log₃x = y

C: log_x3 = y

D: log₃y = x

3) The value of log 0.001 is

A: 3

B: -3

C: 2

D: -2

4)  3log2 + log200 – log16 when evaluated is

A: 2

B: 3

C: 25

D: 75

5) Given that log8 = 0.9030, then log √2 is

A: 0.3010

B: 0.4515

C: 0.1505

D: 0.2150

6) The value of  (log16 – log2)/(log2 + log1) is

A:  4

B: log14/log3

C:  3

D: log8/log3

7) The value of 2log₉9 is

A: 1

B:  0

C: 81

D: 2

8) The value of log√2 is

A:  1

B: 0

C: 1/√2

D:  (√2)²

9) Given that log5 = h and log3 = K, then log45 is

A: h + x

B: 3h + k

C: h + 2k

D: h – k

10) The value of x in log₂(4x + 8) = 2 is

A: 2

B: -4

C: 3

D: -1

SECTION B: Indices

1)  Give that aⁿ x a^m = x, then x in index form is

A: a^nm

B: a^n-m

C: a^n+m

D:  a^n/m

2)  The value of 9^x x 3^x / 27^x is:

A: 0

B:1

C: 2

D: 3

3) The value of (0.003 X 500000)⁰ is

A: 0

B: 1

C: 1500

D: 300

4)  (5125 x 8)^2/3 when simplified is

A: 1000

B: 1

C: 100

D: 300

5) Given that 8^x = 128, then the value of ^x is

A: 7/3

B: 16

C: 3

D: 8/3

6) The values of  x and y that satisfy the equations 8^4+x = 2^1-y and 3^x+1 = 9^-y are respectively

A:  4, 2

B: 1, -2

C:  3, -2

D: 5, – 1

7) If 2^2x = 32^x+1, the value of x is

A: 1

B:  5

C: -3/7

D: -5/3

8) The value of  x in the equation 3^x = 7 is?

A:  7/3

B: log7/log3

C: 3/7

D:  log3/log7

9) (27x²)^-3 / (81x³)^-2 when simplified is

A: 2

B: 3

C: 1/2

D: 1/3

10) (625/400)^-1/2 when simplified gives

A: 64/125

B: 5/4

C: 125/64

D: 4/5