Math

Compare the graphs of the logarithmic functions f(x)= log(7)x and g(x) = log(4)x.
For what values of x is f=g, f>g, and f<g? Explain how you know.

I already know what x is for f=g and f>g, but what is f<g? And how do I explain all this?

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  1. For easier comparison, let's have the same base for both log functions.
    recall : log a b = log b/loga or lnb/lna

    so f(x) = log7x = logx / log7
    = (1/log7) logx
    = appr 1.18329.. logx

    g(x) = log4 = logx/log4
    = appr 1.66096.. logx

    Assuming you got x=1 giving you equality of the two,

    remember that log(any number > 1) is positive,
    and log7 > log4, and logx would be the same for both.
    What division result would give you a larger answer ?

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