Question 1204752
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If 6^(2x+1) = k, then 6^(4x+3) equals
A 12k
B k^2 + 6
C 6k^2
D 2k + 6
E 36k^2
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<pre>
  {{{6^(4x+3)}}} = trace/watch attentively each and every my step = 

= {{{6*6^(4x+2)}}} = {{{6*6^(2*(2k+1))}}} = {{{6*(6^(2k+1))^2}}}  = {{{6*k^2}}}.


<U>ANSWER</U>.  Option (C).
</pre>

Solved.


Is everything clear to you from my solution ?



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In this problem, &nbsp;we have a given basic equation &nbsp;&nbsp;{{{6^(2x+1)}}} = k &nbsp;&nbsp;and an expression to evaluate &nbsp;&nbsp;{{{6^(4x+3)}}}.


An idea of the method is to transform the given "expression to evaluate" step by step to get the given basic expression 

in it somewhere on the way, &nbsp;and then to replace one side of the given basic expression by its other side.


Then a miracle will happen literally in front of your eyes and you will get the required proof 
(or evaluation, &nbsp;or reduction) &nbsp;in minutes &nbsp;(&nbsp;!&nbsp;)



If you will solve such problem once in your life &nbsp;(or if somebody will show you this trick
once in your life, as I do it here for you), &nbsp;you will &nbsp;MEMORIZE &nbsp;it and will be able to repeat it 
in hundreds other similar problems/cases in your life.


It is worth to memorize &nbsp;HOW &nbsp;it works &nbsp;-  &nbsp;then you will have a wonderful mathematical weapon in your possessions &nbsp;(&nbsp;!&nbsp;)



In his post, &nbsp;tutor @math_tutor2020 &nbsp;repeated my solution practically with no change - thanks to him for it,

even although he did not mention about it. &nbsp;Probably, &nbsp;he forgot to mention, &nbsp;or couldn't find the right/appropriate words.


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Dear tutor @math_tutor2020, when I tell about mentioning, I worry not about my rights.
I worry about a reader / (a student): what he will think by seeing 
two identical texts in one post ? - At least, he will have mess in his/her mind.


It is what I'd like to avoid.