Question 30094
{{{0.04^X *10^9 = 1}}}
take logs (to the base 10) of both sides
{{{log((0.04^X * 10^9)) = log(1)}}}
Rule of logs: {{{log((a*b)) = log((a)) + log((b))}}} (to any base)
So we get,
{{{log((0.04^X)) + log((10^9)) = 0}}} (log(1) = 0)
Rule of logs: {{{log((a^b)) = b*log((a))}}} (to any base)
So we get,
{{{X * log((0.04)) + 9 * log((10)) = 0}}}
{{{X*log((0.04)) + 9 = 0}}} (log(10) = 1)
{{{X*log((0.04)) = -9}}}
{{{X = (-9)/log((0.04))}}}
{{{X = (-9)/(-1.39794)}}}
{{{X = 6.4380}}}
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