Question 1098789
.
<pre>
Check your line 1.    


I think that it must be 


{{{3*(3^(2x)) - 28*3^x + 9}}} = 0.   (In plain text format form  it is  3*(3^(2x)) - 28*3^x + 9 = 0.)


If it is so, then it is a quadratic equation relative {{{3^x}}}.
</pre>


For many solved problems of this type (your samples) 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.



-------------
Comment from student: No. Equation is written as in the textbook. It is a lesson not on quadratic equations but on exponential equations. Thank you for the link.
-------------



<U>My response</U>.  Below is the plot of the function in the lft side of your 1-st line.



{{{graph( 330, 330, -10.5, 10.5, -100.5, 100.5,
          3*(3^2)*x - 28*(3^x) + 9
)}}}


Plot y = 3(3^2x) - 28(3^x) + 9 = {{{3(3^2x) - 28(3^x) + 9}}}




There is NO ANY SENSE to argue with me.