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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
Logs practice. [48 marks] 1. Solve the equation 2 ln x = ln 9 + 4 . Give your answer in the form. x = peq where p, q ∈ Z+ . [5 marks] 3. Solve the equation log3 √x = 1 + log3(4x3) , where x > 0 . 2log23. [5 marks] ( )= log ( − 4) > 4 > 0. Let f(x)= a log3(x − 4) , for x > 4 , where a > 0 . Point A(13,7) lies on the graph of f . 3a.
Logarithms Practice Test. Multiple Choice. Identify the choice that best completes the statement or answers the question. ____ 1. Which of the following statements is true? The domain of a transformed logarithmic function is always {x ∈ R}. Vertical and horizontal translations must be performed before horizontal and vertical stretches/compressions.
Having previously defined what a logarithm is (see the notes on Functions and Graphs) we now look in more detail at the properties of these functions. The relationship between logarithms and exponentials is expressed as:
Solve each of the following equations, leaving your final answers as expressions involving natural logarithms in their simplest form. a)e 164x=. b)2e 1 1273y− =. c)3e 5 142. z. d)4. 24 1 25e 25 − =−w.
Collection of logarithms exam questions for practice and revision.
The document was created by T. Madas and provides a full exam on logarithmic concepts and skills. This document contains 27 multiple choice questions about logarithms. The questions cover topics like simplifying logarithmic expressions, solving logarithmic equations, and modeling exponential growth.
