How do you simplify #e^(-2ln5)#?

1 Answer
May 30, 2017

Answer:

0.04

Explanation:

We have,

#e^(-2ln5)= e^(ln(5^-2))=5^-2=1/5^2=1/25=0.04#

Using the following properties of logarithms and exponentials,

#1.# #n*ln# #(m)=ln# #(m^n)# ; #color(blue)(Here)# #color(blue)(Put)# #color(blue)(n=-2)# #color(blue)(and)# #color(blue)(m=5)#

and

#2.# #e^(ln(a))=a# ; #color(blue)(Here)# #color(blue)(Put)# #color(blue)(a=5^-2)#