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  • Exponents and Logarithms
  • Logarithm tests
  • Logarithm definition

Logarithm definition

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  • Question 1:
    1 pts
    Logarithmic functions is the inverses of exponential functions.
  • Question 2:
    1 pts
    logb(x)=yby=x\log_{b}(x)=y\Leftrightarrow b^{y}=x
  • Question 3:
    1 pts
    If f(x)=axf(x)=a^{x} and g(x)=logaxg(x)=\log_{a}x then ff and gg have the same domain.
  • Question 4:
    2 pts
    log17=log1017\log 17= \log_{10}17
  • Question 5:
    2 pts
    Find the inverse of the exponential function 2x=8.2^{x}=8.

    x=log28x=\log_{2}8

    x=log82x=\log_{8}2

    2=logx82=\log_{x}8

    8=log2x8=\log_{2}x

  • Question 6:
    2 pts
    Find the inverse of the exponential function y=3x.y=3^x.

    x=logy3x = log_y3

    x=3logyx = 3logy

    x=log3yx = log_3y

    x=ylog3x = y log3

  • Question 7:
    2 pts
    Find the domain of the function given by y=log(4x2)3y=\log\left(\dfrac{4-x}{2}\right)-3
    (4,+)(4,+\infty)
    (,4)(-\infty,4)
    (4,4)(-4,4)
    (4,+)(-4,+\infty)
  • Question 8:
    3 pts
    Find the correct logarithmic equation. π4=x\pi^{4}=x

    log4x=π\log_{4}x=\pi

    logπ4=x\log_{\pi}4=x

    logxπ=4\log_{x}\pi=4

    logπx=4\log_{\pi}x=4

  • Question 9:
    3 pts
    Find the correct exponential equation. log7x=5\log_{7}x=5

    x=57x = 5^{7}

    x=75x = 7^{5}

    7x=57^{x}=5

    7x5=77x^{5}=7

  • Question 10:
    3 pts
    Solve. log2x=9\log_{2}x=9
    22
    99
    x=81x=81
    x=512x=512
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