Question 1202796
<br>
The use of "^" with logarithms is not standard, and rather confusing....<br>
In words, the equation is "log base 2 of x, plus log base x of 2, equals 5/2".<br>
{{{log(2,x)+log(x,2)=5/2}}}<br>
{{{log(2,x)}}} and {{{log(x,2)}}} are reciprocals.<br>
The sum, 5/2, is 2 + 1/2; and those are reciprocals.<br>
So we have either...<br>
(1)
{{{log(2,x)=2}}}
{{{x=2^2=4}}}
{{{log(x,2)=log(4,2)=1/2}}}<br>
or<br>
(2)
{{{log(2,x)=1/2}}}
{{{x=2^(1/2)=sqrt(2)}}}
{{{log(x,2)=log(sqrt(2),2)=2}}}<br>
ANSWERS:
{{{x=4}}}
{{{x=sqrt(2)}}}<br>