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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?