Math Xb—Spring 2004Properties of LogarithmsNote that log x = log10x and exp(x) = ex.1. Find the expression that is equivalent tolog x + log x2− 3 log x.(a) log(x3+ x − 3)(b) 0(c) logx33(d) logx2+ x3x(e) 12. Find the expression that is equivalent tolog2u2v.(a) log2u + log2v(b) log22 + log2u + log2v(c) 2 log2u + log2v(d) 2 log2u + 2 log2v(e) 1 + log2u + log2v3. Find the expression that is equivalent tolne√uv.(a)12−12ln u −12ln v(b) −√ln u −√ln v(c) 1 −12ln u −12ln v(d) −12ln u −12ln v(e) 1 −√ln u −√ln v14. Find the expression that is equivalent to5 log53√5.(a) 5/3(b) 3/5(c) 60(d) 10(e) 65. Find the expression that is equivalent toln√x −ln x33− 3 ln x.(a)27ln x(b) −27ln x(c)176ln x(d)72ln x(e) −72ln x6. Find the expression that is equivalent tolog23.(a)ln 2ln 3(b) (ln 2)(ln 3)(c) (log 2)(log 3)(d)log 2log 3(e)ln 3ln 27. Find the expression that is equivalent tolog 50.(a) 2 − log 2(b)12log 100(c) log 2(d) log 100 + log 2(e) 2 + log 228. Find the expression that is equivalent to5 log23.(a) log 10 − log 15(b) 5 log 2 − 5 log 3(c) log 15 − log 10(d) 5 log 3 − 5 log 2(e) 5 log 3 + 5 log 29. Find the expression that is equivalent tolog275.(a)ln 5 − ln 2ln 7(b)ln 2 − ln 5ln 7(c)ln 7 − ln 5ln 2(d)ln 5 − ln 7ln 2(e)ln 2 − ln 7ln 510. Find the expression that is equivalent tolog75x.(a)ln 7 + ln xln 5(b)ln 5 + ln xlog75(c)ln 5 + ln xlog57(d)ln 5 + ln xln 7(e)ln 7 + ln 5ln xAnswers1. b2. c3. c4. a5. e6. e7. a8. b9. c10.
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