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 #n#th 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