How to do this question in relations to logs?

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1 Answer
Jim G.
Mar 1, 2018

#"see explanation"#

Explanation:

#"using the "color(blue)"laws of logarithms"#

#•color(white)(x)logx^nhArrnlogx" and "lne=1#

#•color(white)(x)e^(lnx)=x" and "e^(-lna)=e^ln(1/a)#

#"substitute the given points into the equation"#

#(3,50)to50=ae^(-3b)to(1)#

#(6,10)to10=ae^(-6b)to(2)#

#"divide equation "(1)" by equation "(2)#

#50/10=(ae^(-3b))/(ae^(-6b))#

#rArre^(3b)=5#

#rArr3bcancel(lne)^1=ln5#

#rArrb=ln5/3#

#"substitute "b=ln5/3" into equation "(2)#

#10=ae^((-6xxln5/3))=ae^(-2ln5)=ae^(ln(1/25))#

#rArr1/25a=10rArra=250#

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