Concept and Relationship with Quadratic Equation

Exponential or Indicial Equation is a combination of indices and all other forms of equations, it is very easy to solve provided you have excellent knowledge of the laws of Indices.

Rules for Solving Exponential (Indicial) Equations

1. The two sides i.e LHS and RHS of the equation must be expressed in index form.

2. The two sides of the equation must also have the same values for you to cancel them out.

3. You’ll always solve for an unknown value which can be represented by any letter of the alphabet.

Note

You will need to master all the laws of indices, if you must properly understand exponential equations.

Examples

1. If 3² = 3², find x.

Solution

3² = 3²

Step 1

Note that the equations above are already expressed in index form, so just cancel the similar ones out;

3 cancels 3.

x = 2.

2. If 2^{x + 1} = 2³, find x.

Solution

2^{x + 1} = 2³

Step 1

The equation is already in index form, so just cancel out the similar ones;

2 cancels 2;

x + 1 = 3

Step 2

Make x the subject by carrying +1 to the RHS;

x = 3 – 1

x = 2.

3. If 3^x = 9, solve for x.

Solution

3^x = 9

Read more below-

SS 2 Mathematics Third Term Indicial Equation