Question 469699
{{{ d = C*n^(-2) }}}
(a)
Solve for {{{n}}}
Take the log of both sides
using the rule:
{{{ log(a^b) = b*log(a) }}}
{{{ log(d) = (-2)*C*log(n)  }}}
{{{ log(n) = log(d) / (-2*C) }}}
Now use the above rule in reverse
{{{ log(n) = log(d^(1/(-2C)) }}}
Use the rule:
If {{{ log(a) = log(b) }}},
then {{{ a = b }}}
{{{ n = d^(1/(-2C)) }}}
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(b)
{{{ d = 84 }}}
{{{ n = 4480 }}}
Find {{{C}}}
{{{ n = d^(1/(-2C)) }}}
{{{ 4480 = 84^(1/(-2C)) }}}
Let {{{ 1/(-2C) = x }}}
{{{ 84^x = 4480 }}}
{{{ x*log(84) = log(4480) }}}
{{{ x = log(4480) / log(84) }}}
{{{ x = 3.6513 / 1.92428 }}}
{{{ x = 1.8975 }}}
{{{ 1/(-2C) = 1.8975 }}}
{{{ -2C = 1/1.8975 }}}
{{{ C = -1/3.7950 }}}
{{{ C = -.2635 }}}