Αποτελέσματα Αναζήτησης
Question 1 Simplify each of the following logarithmic expressions, giving the final answer as a single logarithm. a) log 7 log 22 2+ b) log 20 log 42 2− c) 3log 2 log 85 5+ d) 2log 8 5log 26 6− e) log 8 log 5 log 0.510 10 10+ − log 142, log 52, log 645, log 26, log 8010
After reading this text and / or viewing the video tutorial on this topic you should be able to: explain what is meant by a logarithm. state and use the laws of logarithms. solve simple equations requiring the use of logarithms.
8. Prove the following statements. (1) logp b x = 2log x (2) log p1 b p x = log x (3) log 4 x2 = log p x 9. Given that log2 = x, log3 = y and log7 = z, express the following expressions
Condense each expression to a single logarithm. 13) log 3 − log 8 14) log 6 3 15) 4log 3 − 4log 8 16) log 2 + log 11 + log 7 17) log 7 − 2log 12 18) 2log 7 3 19) 6log 3 u + 6log 3 v 20) ln x − 4ln y 21) log 4 u − 6log 4 v 22) log 3 u − 5log 3 v 23) 20 log 6 u + 5log 6 v 24) 4log 3 u − 20 log 3 v Critical thinking questions:
log . . . = logbX – logbY. logb(XY) = logbX + logbY Power Rule for Logarithms. Quotient Rule for Logarithms. Product Rule for Logarithms. The following examples show how to expand logarithmic expressions using each of the rules above.
Properties of Logarithms Expand each logarithm. 1) log (6 ⋅ 11) 2) log (5 ⋅ 3) 3) log (6 11) 5 4) log (3 ⋅ 23) 5) log 24 5 6) log (6 5) 6 7) log x y6 8) log (a ⋅ b)2 9) log u4 v 10) log x y5 11) log 3 x 12) log⋅ y ⋅ z (x ⋅y z2) 1-
This document contains 27 multiple choice questions about logarithms. The questions cover topics such as simplifying logarithmic expressions, solving logarithmic equations, and modeling exponential growth.
