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:

5

^{2x}- 26(5

^{x}) + 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

Q

^{2}+ BP + C

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

let implement that;

let P=5

^{x}

WE REWRITE THE EQUATION AS

5

^{X(2)}- 26(5

^{X}) + 25 = 0

P

^{2}- 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 =5

^{X}

WHEN P is 1 we have

1 = 5

^{x}

5

^{x}=1

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

use logarithm.

5

^{x}=1=5

^{0}

so x=0

When x is 25, we have

5

^{x}= p

5

^{x}=25=5

^{2}

5

^{x}=5

^{2}

x=2

then you write your final staement as

x=0 or 2

QUESTION 2

5

^{2x + 1}- 26(5

^{x}) + 5 = 0

Let recall one of the law of indices

where we have

x

^{a+b}=x

^{a}* x

^{b}

5

^{2x}* 5

^{1}- 26(5

^{x}) + 5 =0

let continue with this

(5

^{x})

^{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=5

^{x}

When P= 1/5

we have

1/5 = 5

^{x}

1/5=5

^{-1 }= 5

^{x}

5

^{-1}= 5

^{x}

x= -1

then, when P=5, we have

5=5

^{x}

5=5

^{1}=5

^{x}

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

22

^{x }- 6(2

^{x}) + 8 = 0

22

^{x}+ 1 - 5(2

^{x}) + 2 = 0

32

^{x}- 9 = 0

72

^{x}- 2(7

^{x})+ 1 = 0

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