Question 972081
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If 7^(2x)=3 What is the value of 7^(6x-1)?
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        The answer in the post by @lwsshak3 is incorrect (numerically wrong),

        and the way how he solves the problem is not which is expected.


        A standard method is different.



<pre>
{{{7^(6x-1)}}} = {{{(7^(6x))/7}}} = {{{((7^(2x))^3)/7}}} = now replace here {{{7^(2x)}}} by 3, as it is given, and continue = {{{3^3/7}}} = {{{27/7}}} = 3.857142857 (approximately)


<U>ANSWER</U>.  The exact value is  {{{27/7}}}.  The decimal approximation is 3.857142857.
</pre>

Solved correctly.


This way is what a teacher expects to get from a student - not the way which @lwsshak3 uses in his post.


For this problem and for many other similar problems the expected way is to build a chain of identities, 
starting from the expression you want to evaluate and ending the exact numerical value, such that the given 
equality is a link in this chain.