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Logarithmic Functions

Please see the attached file for the fully formatted problems.

1. Use the change of base formula to find the following logarithm. Round to five decimals.

2. Solve for x in each of the following equations below. Give the exact answer when possible. If no exact answer is possible, round your answer to 5 decimals.


(b) log(x + 1) ? log(x ? 4) = log 6 (c) (exact)

3. NO CALCULATOR allowed: Use techniques of transformation and rules of logarithms to find domain, range, intercepts and the equation of the vertical asymptote for the following function:

f(x) = log 5 (x + 2)

a) What action was used to transform y = log 5 (x) into the new function?

b) Find the Domain of the new function:

c) Find its Range:

e) Provide the coordinates of its x-intercept:

f) Find the equation of the Vertical Asymptote:

g) What are the coordinates of the y-intercept of the new function?

h) Graph:

4. Write the following statement in logarithmic form:

5. Word Problem: Since Bluefin tuna are used for sushi, a prime fish can be worth over $30,000. As a result, the western Atlantic bluefin tuna have been exploited, and their numbers have declined exponentially. Their numbers in 1000s from 1974 to 1991 can be modeled by N(t) = 230(0.881)x , where x stands for years and x = 0 corresponds to 1974.

(a) To the nearest whole number estimate the number of Bluefin tuna in 1974 and 1991.

(b) Find the year when their numbers were 50,000. Set up and solve an appropriate equation.


Solution Summary

Logarithmic functions are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.