Question 1111532
.
<U>Obvious &nbsp;answer</U>.  &nbsp;&nbsp;x = 0.2.


<U>Solution</U>


<pre>
Introduce new variable  u = {{{6^(5x)}}}.


Then your equation becomes

{{{u^2 - u - 30}}} = 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 = {{{6^(5x)}}},   only positive root  works  u = 6,


which gives  {{{6^(5x)}}} = 6;   Hence,  5x = 1  and  x= 0.2.
</pre>

Solved.


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


See the lesson 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/How-to-solve-exponential-equations.lesson>Solving exponential equations</A>

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


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



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.