How do you solve #4^(-3t)=0.10#?

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Answer 1 · 2018-05-19T14:18:47

#4^(-3t)=0.10#

#4^(-3t)=0.10#
#ln(4^(-3t))=ln(0.10)#
#-3 t*ln(4)=ln(0.10)#
#t=- ln(0.10)/(3*ln(4))#

Answer 2 · 2018-05-19T14:19:30

#t=-log0.1/(3log4)~~0.55#

Given: #4^(-3t)=0.1#

Take logarithms on both sides.

#log(4^(-3t))=log0.1#

#=>-3tlog4=log0.1#

#=>-3t=log0.1/log4#

#t=-1/3log0.1/log4#

#t=-log0.1/(3log4)#

#~~0.55#