Functions with Base b

Key Questions

  • What are some identity rules for logarithms?

    Log/Exp Inverse Properties

    b^{log_b x}=x

    log_b b^x=x

    Other Log Properties

    log_b(xcdot y)=log_b x+log_b y

    log_b(x/y)=log_b x-log_b y

    log_b x^r=r log_b x

    I hope that this was helpful.

    Wataru · · Oct 20 2014
  • What is the exponent rule of logarithms?

    Answer:

    log_(a)(m^(n)) = n log_(a)(m)

    Explanation:

    Consider the logarithmic number log_(a)(m) = x:

    log_(a)(m) = x

    Using the laws of logarithms:

    => m = a^(x)

    Let's raise both sides of the equation to nth power:

    => m^(n) = (a^(x))^(n)

    Using the laws of exponents:

    => m^(n) = a^(xn)

    Let's separate xn from a:

    => log_(a)(m^(n)) = xn

    Now, we know that log_(a)(m) = x.

    Let's substitute this in for x:

    => log_(a)(m^(n)) = n log_(a)(m)

    Tazwar Sikder · 1 · Sep 16 2016
  • What does a logarithmic function look like?

    Answer:

    The reflection of the exponential function on the axis y=x

    Explanation:

    Logarithms are the inverse of an exponential function, so for y=a^x, the log function would be y=log_ax.

    So, the log function tell you what power a has to be raised to, to get x.

    Graph of lnx:
    graph{ln(x) [-10, 10, -5, 5]}

    Graph of e^x:
    graph{e^x [-10, 10, -5, 5]}

    Karthik N · 1 · May 1 2018

Questions

Properties of Logarithmic Functions