Evaluate the following expressions a e4 ln 4 b 102 log105

Evaluate the following expressions. (a) e^4 ln 4 = (b) 10^2 log_10^5 = (c) log_2 8^4 =

Solution

a) e^4ln(4) = y

take natural log on both sides:

4ln4 = lny

ln(4^4) = lny

y = 256

b) 10^(2log10(5)) = y

take log on both sides:

2log10(5)*log10 = logy

2log10(5) = logy

log10(5^2) = logy

log10(25) = logy

y = 25

c) log2(8^4) = y

8^4 = 2^y

(2^3)^4 = 2^y

2^12 = 2^y

y = 12