CHAPTER 13 REVIEW EXERCISES

Concept check Exercises

Determine each of the following as being either true or false. If it is false, explain why.

  1. y =  − 6 − x is an exponential function.

  2. The logarithmic form of y =  − 2 − x is x =  − log − 2y . 

  3. log45 = log 4log 5

  4. log(1100) =  − 2

  5. 2 ln x = ln x2 − ln e

  6. If 2 ln x − 1 = ln x ,  then x = e . 

Practice and Applications

In Exercises 7–18, determine the value of x.

  1. log10x = 4

  2. log9x = 3

  3. log5x =  − 1

  4. log4(sin x) =  − 0.5

  5. 2 log1/28 = x

  6. log12144 = x − 3

  7. log832 = x + 1

  8. log927 = x

  9. logx36 = 2

  10. logx(1/243) = 5

  11. logx10 = 13

  12. logx8 = 0

In Exercises 19–30, express each as a sum, difference, or multiple of logarithms. Wherever possible, evaluate logarithms of the result.

  1. log36x

  2. log5(7a3)

  3. log3(t2)

  4. log65

  5. log2

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