let f(x) = log3 x/2 + log3 16 - log3 4 for x>0?

a. show that f(x) = log 3 2x.

b. find the value of f(0.5) and of f(4.5)

The junction f can also be written in the form f(x)=ln ax/ln b

c. i. Write down the value of a and of b

ii. write down the equation of the asymptote.

d. write down the value of f-1(o)

2 Answers

Relevance
  • tc
    Lv 7
    8 years ago

    f(x) = log₃ x/2 + log₃ 16 - log₃ 4

    = log₃(x/2 * 16 /4)

    = log₃(2x)

    f(0.5) = log₃(1) = 0

    f(4.5) = log₃(9) = log₃ 3² = 2

    f(x)=ln ax/ln b = ln 2x / ln 3

    a = 2

    b = 3

    VA : x = 0

    f-1(0)

    => 0 = log₃(2x)

    3⁰ = 2x = 1

    x = 1/2

Still have questions? Get your answers by asking now.