Let's make it easy to solve 'Indices Equation'...u just remember 3 types of indices equation...
First : By equating the base
a^x = a
Example:
Solve the equation of 2^(x+1) = 4^x
Solution2^(x+1) = 4^x
2^(x+1) = 2^(2x)
x+1 = 2x
Therefore, x = 1
Second : Using Logarithm
a^x = b
Example:
Solve the equation 5^x = 8
Solution:
5^x = 8
log 5^x = log 8
x log 5 = log 8
x = log8/log5
Therefore, x = 1.292
Third : Factorise
a^x +ba^x + c
Example :
Given 2^(2x) - 5(2^x) + 4 = 0. Find the value of x
Solution:
2^(2x) - 5(2^x) + 4 = 0
(2^x)^2 - 5(2^x) + 4 = 0
Replace y = 2^x
y^2 - 5y + 4 = 0
(y - 1)(y - 4) = 0
y = 1 or y = 4
2^x = 1 2^x = 4
2^x = 2^0 2^x = 2^2
x = 0 x = 2