1 Use the Laws of Logarithms to evaluate the expression log5

#1 Use the Laws of Logarithms to evaluate the expression.

log₅(14) log₅(10) log₅(35)

(an exact number)

#2 Use the Laws of Logarithms to evaluate the expression.

ln(ln(e^e400))

(an exact number)

Solution

1) log₅(14) log₅(10) log₅(35)

Laws of logarithm : logx - logy = log(x/y)

So, log5(14/10*35) = log5(2/50)

= log5(1/25)

= log5(5^-2)

= -2

2) ln(ln(lne^(e^400)) )

= ln(ln(e^400ln(e))) -----> ( lne =1 )

= ln( ln(e^400))

= ln(400ln(e))

= ln(400) ------> ( lne =1)

from calculator :

= ln400 = 5.99 = 6