Question 638062
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Can you please help me evaluate 5^log1/5(1/2)
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<pre>
Let  {{{log(1/5,(1/2))}}} = x. 


It means that  {{{(1/5)^x}}} = {{{1/2}}}.


This last equation is equivalent to  {{{5^x}}} = 2.


It means that  x = {{{log(5,(2))}}}.


Thus  {{{5^log(1/5,(1/2))}}} = {{{5^log(5,2)}}}.


But  {{{5^log(5,2)}}}  is  2, due to the definition of the logarithm.


<U>ANSWER</U>.  {{{5^log(1/5,(1/2))}}} = 2.


At this point, the problem is solved completely.


We evaluated  {{{5^log(1/5,(1/2))}}}  and found out that the value is 2.
</pre>

Solved.



This my solution is to replace the solution by tutor @Theo.