Find the value of each of the following if not applicable en

Find the value of each of the following, if not applicable enter NONE

log(10^2) (j) log(1000) (k) log(0.0001) (I) e^ln(5) (m) ln(e^4/5) (n) ln(e^-4) (o) e^(2 + In(7))

Solution

i) . log(10^2) = 2log10 [ by formula log a^m = m loga]

=2x1 [ since log10=1 ]

=2

j) log(1000) = log(10^3)

= 3

k). log (0.0001) = log(10^-4)

= -4x1 = -4

l) . e^ln(5) = 5

m) ln(e^4/5) = 4/5 ln(e) [ by ln a^m = m ln a]

= 4/5 [ since ln e=1 ]

n). ln(e^-4) = -4 ln e

=-4

0). first

2 + ln(7) = ln e^2 + ln(7) = ln [ e^2 7]

so e^(2 +ln(7) = e^ ln(e^2.7)

= e^2.7

= 7 e^2