Question 1205555
<br>
{{{log8(log5x) = 0}}}<br>
The format of the given equation is poor, allowing different interpretations. You/we can only guess what the intended equation is supposed to be.<br>
One tutor interpreted it like this:<br>
{{{(log((8)))(log((5x)))=0}}}<br>
That says the product of two expressions is zero.  {{{log((8))}}} is not zero, so {{{log((5x))}}} must be zero; that makes 5x = 1 and x = 1/5.<br>
The probable intended interpretation is as shown by the other tutors:<br>
{{{log(8,(log(5,(x))))=0}}}<br>
That leads to {{{log(5,(x))=8^0=1}}}, which leads to x = 5^1 = 5.<br>
Yet another possible (and less likely) interpretation is this:<br>
{{{log(8,(log((5x))))=0}}}<br>
That leads to {{{log((5x))=8^0=1}}}.  With no base defined, that leads to {{{log(10,((5x)))=1}}}, which leads to 5x = 10^1 = 10 and x = 2.<br>