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 logb x. In algebraic terms this means that
if y = logb x then
x = by
The formula y = logb 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 = logb x and x = by are equivalent statements.
Example 1 :
If log4 x = 2 then
x = 42
x = 16
Example 2 :
We have 25 = 52.
Then log5 25 = 2.
Example 3 :
If log9 x = 1/2 then
x = 9 1/2
x = √9
x = 3
Example 4 : If log2 (y/3) = 4 then
y/3 = 24
y/3 = 16
y = 48
Solve the following:
(a) log3 x = 4
(b) logm 81 = 4
(c) logx 1000 = 3
(d) log2 (x/2) = 5
(e) log3 y = 5
(f) log2 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