Question 322086
<pre><b>
{{{log(7,(9))log(5,(7))log(3,(5))}}}

Use the change of base formula {{{log("OLD_BASE",(X))}}}{{{"="}}}{{{log("NEW_BASE",(X))/log("NEW_BASE",("OLD_BASE"))}}} 

for each of those logarithms:

{{{

(log(10,(9))/log(10,(7)))

(log(10,(7))/log(10,(5)))

(log(10,(5))/log(10,(3)))

}}}

Write {{{9}}} as {{{3^2}}}

{{{

(log(10,(3^2))/log(10,(7)))

(log(10,(7))/log(10,(5)))

(log(10,(5))/log(10,(3)))

}}}




Use the rule of logarithms: {{{log(B,(Y^X))}}}{{{"="}}}{{{X*log(B,Y)}}} to rewrite the leftmost numerator:

{{{

(2*log(10,(3))/log(10,(7)))

(log(10,(7))/log(10,(5)))

(log(10,(5))/log(10,(3)))

}}}

Everything cancels but the 2

{{{

(
2*cross(log(10,(3)))
/
cross(log(10,(7)))
)

(
cross(log(10,(7)))
/
cross(log(10,(5)))
)

(
cross(log(10,(5)))
/
cross(log(10,(3)))
)

}}}

Answer: 2

Edwin</pre>