How do you solve #400(1-0.2)^x=50#?

1 Answer
Guillaume L.
May 9, 2018

#x=ln(8)/ln(5/4)#

Explanation:

#400(1-0.2)^x=50#
#ln(400(1-0.2)^x)=ln50#
#lnab=lna+lnb#
#ln400+ln(0.8^x)=ln50#
#lna^b=blna#
#ln400+xln0.8=ln50#
#xln0.8=ln(50/400)#
#xln0.8=ln(1/8)#
#cancel(-)xln(5/4)=cancel(-)ln8#
#x=ln(8)/ln(5/4)#
\0/ here's our answer!

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