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A logarithm answers the question: “To what exponent do I need to raise a given base to get a certain number?” For instance, if we have 2 3, the logarithmic equivalent would be log 2 (8) = 3. In this case, the logarithm tells us that we need to raise 2 to the power of 3 to get 8. The general form of a logarithm is written as: log b (y) = x
Logarithms. The mathematics of logarithms and exponentials occurs naturally in many branches of science. It is very important in solving problems related to growth and decay. The growth and decay may be that of a plant or a population, a crystalline structure or money in the bank.
Simplify each of the following logarithmic expressions, giving the final answer as a single fraction. a) log 24 b) log 84 c) log 2 24 ( ) d) 5 1 log 125 1 2, 3 2, 3 4, 3 2 −
Logarithms Study Development Worksheet Answers 1. Using log laws or a calculator, we find: i) )𝑙 𝑔4(16=2 ii) (𝑙 𝑔232)=5 iii) 𝑙 𝑔3(1 3)=𝑙 𝑔3(1)−𝑙 𝑔3(3)=0−1=−1. Alternatively, you may already know that 3−1=1 3, in which case you do not need to separate the logs out. iv) (𝑙 1)=0 v) )𝑙 (10=2.303
11. Draw the graph of each of the following logarithmic functions, and analyze each of them completely. (1) f(x) = logx (2) f(x) = log x (3) f(x) = log(x 3) (4) f(x) = 2log 3 (3 x) (5) f(x) = ln(x+1) (6) f(x) = 2ln 1 2 (x+3) (7) f(x) = ln(2x+4) (8) f(x) = 2ln( 3x+6)
Students will solve problems for various logarithmic forms from finding the range, inverse functions, domains, and writing equal statements. Ten problems are provided. Review and Practice. This worksheet reviews all the various skills we have seen so far with logarithmic functions.
Definition 1: The logarithm with base 10 is called the _____ logarithm. o The base does not need to be shown when writing a common logarithm. o “log x” is understood to mean “log 10 x”. (You do not have to write the 10). o The LOG key on your calculator gives base 10 logarithms. Ex 1: Evaluate log 8 ylog 10
