SOLUTION: 6^10x − 6^5x − 30 = 0

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Question 1111532: 6^10x − 6^5x − 30 = 0
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Obvious  answer.   x = 0.2.

Solution 

Introduce new variable  u = .


Then your equation becomes

 = 0.


Factor left side

(u-6)*(u+5) = 0.


The two roots to the last equation are  u= 6  and  u= -5,


but since u = ,   only positive root  works  u = 6,


which gives   = 6;   Hence,  5x = 1  and  x= 0.2.

Solved.

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Introducing new variable is the STANDARD method of solving exponential equations.

See the lesson
    - Solving exponential equations
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Exponential equations".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


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