Math 121 – Quiz 4 Solution
1. Find the exact value of each logarithm without using a calculator.
(a) log232
(b) ln e4
2. Find the exact solution(s) to the following equation:
ln x+ ln(x+ 2) = 4
Solution:
1. (a) log232 = log225= 5 log22 = 5
(b) ln e4= 4 ln e= 4
2.
ln x+ ln(x+ 2) = 4
ln[x(x+ 2)] = 4
x(x+ 2) = e4
x2+ 2x−e4= 0
x=−2±p22−4(1)(−e4)
2(1)
x=−2±√4 + 4e4
2
x=−1±p1 + e4
Since the domain of ln xis all positive reals, x=−1 + √1 + e4.
