Math 142
Example 1: Solve for x in the equations:
a) log x = −3
.
2
b) ln e2 = x.
Example 2: Evaluate the expressions:
a) log3 3−2
b) 10log 3
c) eln e
Section 1.5 Examples
Math 142
Section 1.5 Examples
Example 3: Evaluate the following (using your calculator) to 2 decimal places:
a) log2 10
b) log5 58
c) loge2 23
Example 4: Write the following using only one logarithm.
a) 2 log x − 31 log y
b) 5 log x − 43 log y + log z
Math 142
Example
5: Write the following quantities in terms of log x, log y, and log z
√
x2 y
a) log z
b) log
q
xy 3
z5
Example 6: Solve the following equations for x.
a) 2 log(2x + 5) + 6 = 0.
b) 5 · 105x = 3.
c) ln x + ln x9 = ln 36
d) log(ln 4x) = 0
Section 1.5 Examples
Math 142
Section 1.5 Examples
Example 7: A bank account is growing at 9% a year compounded continuously. How long does it
take for this account to double?
Example 8: At a different bank, a person invests $1000 at an annual rate of 8% compounded
quarterly. How long will it take for this account to reach $1400?