Question
Compare the graphs of the logarithmic functions f(x) =log7 x and g(x)=log4 x. For what values of x is f=g and f<g? Explain how you know.
Answers
Reiny
I assume you meant
f(x) = log<b>7</b> x and g(x) = log<b>4</b> x
log<b>7</b> x = log<b>4</b> x
I know that all log graphs of the form
y = log<b>a</b> x where a > 0 , a not = 1
pass through the point (1,0)
You should know the basic shape of y = log<b>a</b> x
since log<b>a</b> x = logx/loga
and since log7 > log4 , you know which is the larger value for any logx
f(x) = log<b>7</b> x and g(x) = log<b>4</b> x
log<b>7</b> x = log<b>4</b> x
I know that all log graphs of the form
y = log<b>a</b> x where a > 0 , a not = 1
pass through the point (1,0)
You should know the basic shape of y = log<b>a</b> x
since log<b>a</b> x = logx/loga
and since log7 > log4 , you know which is the larger value for any logx
Reiny
the bold was to be a subscript