Question 1192803
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The first three terms of a geometric sequence are lnx^16, lnx^8, lnx^4, for x>0. Find the common ratio.
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<pre>
The 1-st term is  ln(x^16) = 4*ln(x^4).


The 2-nd term is  ln(x^8) = 2*ln(x^4).


The 3-rd term is  ln(x^4).


The ratio  {{{a[2]/a[1]}}} = {{{1/2}}}.


The ratio  {{{a[3]/a[2]}}} = {{{1/2}}}.


So the progression is geometric and its common ratio is  {{{1/2}}}.    <U>ASNSWER</U>
</pre>

Solved and explained.


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The side note : &nbsp;&nbsp;in this problem, &nbsp;x > 0 &nbsp;&nbsp;IS &nbsp;NOT &nbsp;&nbsp;a necessary condition.  &nbsp;The necessary condition is  &nbsp;&nbsp;| x | =/= +/-1.