Logarithms are very important in solving problems related to growth and decay. Let's learn about it with examples in A-Level Maths!

**Definition**

If x and b are positive numbers and b ≠ 1 then the logarithm of x to the base b is the power to which b must be raised to equal x. It is written log_{b} x. In algebraic terms this means that

**if** **y** **=** **log**_{b} **x** **then**

**x** **=** **b**^{y}

The formula y = log_{b} x is said to be written in logarithmic form and x = by is said to be written in exponential form. In working with these problems it is most important to remember that y = log_{b} x and x = b^{y} are equivalent statements.

Example 1 :

If log_{4} x = 2 then

x = 42

x = 16

Example 2 :

We have 25 = 5^{2}.

Then log_{5} 25 = 2.

Example 3 :

If log_{9} x = 1/2 then

x = 9 ^{1/2}

x = √9

x = 3

Example 4 : If log_{2 }(y/3) = 4 then

y/3 = 2^{4}

y/3 = 16

y = 48

**Solve the following:**

(a) log_{3} x = 4

(b) log_{m} 81 = 4

(c) log_{x} 1000 = 3

(d) log_{2} (x/2) = 5

(e) log_{3} y = 5

(f) log_{2} 4x = 5

Ans:

(a) 81

(b) 3

(c) 10

(d) 64

(e) 243

(f) 8

Drafted by Eunice (Maths)

Reference

https://en.wikipedia.org/wiki/Logarithm