Question 1018108
Hello could you please help me simplify: log little3 3/4+ log little3 4/5+ log little3 5/6+ log little3 6/7+ log little3 7/8+ log little3 8/9 / log 4/5+ log 5/6+ log 6/7+ log 7/8+ log 8/9+ log 9/10
<pre>{{{(log (3, (3/4) * (4/5) * (5/6) * (6/7) * (7/8) * (8/9)))/(log ((4/5) * (5/6) * (6/7) * (7/8) * (8/9) * (9/10)))}}} -------> {{{(log (3, (3/cross(4)) * (cross(4)/cross(5)) * (cross(5)/cross(6)) * (cross(6)/cross(7)) * (cross(7)/cross(8)) * (cross(8)/9)))/(log ((4/cross(5)) * (cross(5)/cross(6)) * (cross(6)/cross(7)) * (cross(7)/cross(8)) * (cross(8)/cross(9)) * (cross(9)/10)))}}} --------> {{{(log (3, (3/9)))/(log ((4/10)))}}} -------> {{{(log (3, (1/3)))/(log ((4/10)))}}}
{{{log (3, (1/3))}}} = - 1
{{{log (4/10)}}} = log 4 - log 10 = log (4) - 1
Thus, {{{(log (3, (1/3)))/(log ((4/10)))}}} becomes: {{{highlight(highlight_green(highlight((- 1)/(log ((4)) - 1)))))}}}