EXPONENTIAL

MATHEMATICS----Exponential Equation

This is well known for it simplicity and quadractic form.It a topic which is one of the topics with

complex but simple question. Except you have a glimpse of what it all about.

example:

52x  -  26(5x)   +   25=0

solution

It simple all you have to know about this before taking any step, is that we must devise a plan to

make the equation like this

Q2 + BP + C

Where Q represents the variable, and B represents the coefficient, and C is the constant.

let implement that;


let P=5x

WE REWRITE THE EQUATION AS

5X(2)  -  26(5X)  +  25  = 0

P2      -   26P     +  25 = 0

THEN, IT TIME WE INPUT OUR KNOWLEDGE ABOUT QUADRACTIC FACTORIZATION

(P-1)(P-25)=  0

so therefore, we have

p=1 or p=25

Then let go back to the question, because we were not asked to look for P; we only diverted and

reconstructed the question inorder to make the question more simple to attempt.We must now find

our X

Recall from the beginning that

P =5X

WHEN P is 1 we have

1 = 5x

5x=1

So it time you reason, and if you are not good in using indices, it more preferrable though stressful to

use logarithm.

5x=1=50 

so x=0

When x is 25, we have

5x= p

5x=25=52

5x=52

x=2

then you write your final staement as

x=0 or 2


QUESTION 2

52x + 1 -  26(5x)  +  5 = 0

Let recall one of the law of indices

where we have

xa+b=xa * xb

52x * 51  -  26(5x) + 5 =0

let continue with this

(5x)2 *  5 - 26(5x)  + 5 =0

Let P =  5x

Note you can make use of any letter to represent it, just that I love to use the letter P

P2 * 5 - 26P  +  5  = 0

THIS SIGN '*' mean multiply, so we have

5P2 -  26P + 5 = 0

When we factorize we have

(5P - 1) (P -5) = 0
So therefore, we have


5P - 1 =0   or P-5=0

when we use the signs law, whenever a negative number crosses the equal to sign '=' it changes to the
opposite number

5P=1  or  P=5

p=1/5 or 5

we have arrived at the building, we now have to find X in the building.

recall:

P=5x

When P= 1/5

we have

1/5 = 5x

1/5=5-1 = 5x

5-1  = 5x

x= -1

then, when P=5, we have

5=5x

5=51 =5x

x=1

then, we write our final statement as

x= -1 or 1

Have this as your class work, or assignment. anyway you see it. But please, submit only your answer

through the comment box.

CLASS WORK
22x - 6(2x)  +  8 = 0
22x + 1  -  5(2x) + 2 = 0
32x - 9 = 0
72x  - 2(7x )+ 1 = 0
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