Chapters

## Exercise 1

Solve the exponential equations:

1

2

3

4

5

6

7

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## Exercise 2

Solve the following exponential equations.

1

2

3

4

5

## Exercise 3

Solve the following exponential simultaneous equations.

1

2

3

## Solution of exercise 1

Now, we will solve the exponential equations from exercise 1 step by step.
1
Since, , hence we can write on the right side of the equation  :

2

We can write the expression as

The resulting expression after simplifying will be:

Cancel 2 from both sides of the equation to get the following answer:

3

We can write the above expression as:

Cancel 2 from both sides of the equation to get:

Divide both sides by 2 and set the equation equal to 0 by taking the constant to the right side of the equation:

Factor the equation like this:

Either or

Hence, or

4
Since, , hence we can write the equation like this: Cancel 2 from both sides of the equation to get the following expression:

5
Take log on both sides:

6
It can be written as:

Take log on both sides of the equation:

7
Take log on both sides of the equation:

## Solution of exercise 2

Solve the following exponential equations.

1

Suppose

Solve the expression by taking L.C.M of the left hand side:

Set the equation to 0 by taking the constant to the left hand side of the equation:

Simplify it further to get the following expression:

Find factors of the above expression like this:

or

or

or

The solution for cannot be determined, hence the exponential equation will have only one solution, i.e.

2
Put

Solve the above expression by factoring like this:

has no solution.

has the solution which is

3

We can write the above expression like this:

Put

4

Suppose

or

## Solution of exercise 3

Solve the exponential simultaneous equations.

1

First, we will simplify the first expression and convert it into linear equation in two variables.

Take the expression from the denominator on the left hand side to the right hand side. Hence, the resultant equation will be:

Now, solve the system of linear equations

Solving the system of linear equations we get the following values for and

and

2

The second expression can be written as:

Put and

The resultant system of equations will be:

Solve the above system of linear equations to get the value of u and v:

and

and

and

3

Since and  , hence we can write the second expression as:

Simplifying both the equations further we will get:

and

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