# Exponential Equation

## Exponential Equation

An equation which contains the unknown variable appearing as an exponent of a base is known as an exponential equation. In the equation 5x = 25, the unknown variable x is an exponent of base 5. So this equation is called an exponential equation. ********************

10 Math Problems officially announces the release of Quick Math Solver, an Android App on the Google Play Store for students around the world.

********************

The axioms given below help to solve the exponential equations:

a)    If xa = ya, then x = y

b)   If xa=xb, then a = b

c)    If xa = 1, then xa = x0. So a = 0

The following steps are useful to solve the exponential equation:

1.    Simplify both sides of the equation

2.    Make both sides of the equation into the same base.

3.    Equate their exponents and simplify.

### Workout Examples

Solution: Here,

a)      2x+4 = 8x

or,     2x+4 = (23)x

or,     2x+4 = 23x

x+4 = 3x

or,     4 = 3x – x

or,     4 = 2x

or,     x = 4/2

or,     x = 2

Example 3: Solve: 32x+1 – 9x+1 + 54 = 0

Solution: Here,

32x+1 – 9x+1 + 54 = 0

or,     32x.31 – 9x.91 = -54

or,     9x.3 – 9x.9 = -54

or,     9x(3 – 9) = -54

or,     9x.-6 = -54

or,     9x = -54/-6

or,     9x = 9

or,     9x = 91

x = 1  or,     25x2 + 25 = 626x

or,     25x2 – 626x + 25 = 0

or,     25x2 – 625x – x + 25 = 0

or,     25x(x – 25) – 1(x – 25) = 0

or,     (x – 25)(25x – 1) = 0

Either, x – 25 = 0

or, x = 25

or, 5a = 52

a = 2

Or, 25x – 1 = 0

or, 25x = 1

or, x = 1/25

or, x = 1/52

or, 5a = 5-2

a = -2

a = 2 or -2

Example 7: Solve: 4 × 3x+1 = 27 + 9x

Solution: Here,

4 × 3x+1 = 27 + 9x

or,     9x – 4 × 3x+1 + 27 = 0

or,     32x – 4 . 3x . 31 + 27 = 0

or,     (3x)2 – 12 . 3x + 27 = 0

Let, 3x = a

Then, a2 – 12a + 27 = 0

or,     a2 – 9a – 3a + 27 = 0

or,     a(a – 9) -3(a – 9) = 0

or,     (a – 9)(a – 3) = 0

Either, a – 9 = 0

or, a = 9

or, 3x = 32

x = 2

Or, a – 3 = 0

or, a = 3

or, 3x = 31

x = 1

x = 1 or 2

You can comment your questions or problems regarding the exponential equations here.

#### 1 comment:

1. When the computer divides the random number by the set worth, it data the remainder of the quotient. In our example, it finds that 64 goes into 123,456,789 a complete of 1,929,012 instances with a remainder of 21. While all of that is occurring, the control cam is slowly returning to its original position. When it does return, it pushes the 1xbet cam plate back, which releases the stoppers. The totally different catches holding onto the totally different stoppers are positioned in order that the cam plate will launch the stoppers one by one. Each stopper springs forward and locks into a notch, holding the reel in position.