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1. Write equation [pic] = 300 in its equivalent logarithmic form.
Solution:
Equivalent logarithmic form will be
[pic]
2. Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator [pic] [pic]
Solution:
[pic]
Answer: [pic]
3. Use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions with out a calculator. 5 [pic] x + 6 [pic] y
Solution:
[pic]
Answer: [pic]
4. Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places [pic]57.2
Solution:
[pic]57.2
= log(57.2)/log(16)
= 1.4595
Answer: 1.4595
5. The loudness level of a sound can be expressed by comparing the sounds intensity to the intensity of a sound barely audible to the human ear. The formula D=10( log I - log [pic]) describes the loudness level of a sound, in watts per [pic], and [pic] is the intensity of a sound barely audible to the human ear.
a. Express the formula so that the expression in parentheses is written as a single logarithm.
Solution:
D=10( log I - log [pic])
[pic]
b. Use the form of the formula from part (a) to answer this question: If sound has an intensity 100 times the intensity of a softer sound, how much larger on the decibel scale is the loudness level of the more intense sound?
Solution:
[pic] watts per [pic]
Answer: 20 watts per [pic]
6. The formula t= [pic][1n A – 1n(A –N)]describes the time t, in weeks, that it takes to achieve mastery of a portion of a task, where A is the maximum learning possible, N is the portion of the learning that is to be achieved, and c is a constant used to measure and individual’s learning style.
A) Express the formula so that the expression in brackets is written as a single logarithm.
Solution:
[pic]
B) The formula is also used to determine how long it will take chimpanzee and apes to master a task. For example, a typical chimpanzee learning sign language can master a max of 65 signs. Use the formula from part (a) to answer this question. How many weeks will it take a chimpanzee to master 30 signs if c for that chimp is 0.03?
Solution:
[pic]
Answer: 20.63 weeks
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