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Compare the graphs of the logarithmic functions f(x)= log7 (x) and g(x)=log4(x) . For what values of x is f=g , f>g, and f

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The blue curve represents the f(x) function while the orange curve represents the g(x) function
f=g, if x<0 and f>g, if x>0
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Answer:

The graph of f(x) and g(x) is defined for x>0 as logarithmic function is always defined for x>0. By looking at the attached graph of f(x)=log(7 x) and g(x)=log(4 x) we could clearly observe that

f(x) and g(x) tends to minus infinity as x tends to zero i.e. f(x)≈g(x) when x→0.

otherwise f(x)>g(x) for x>0.


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