The volleyball team at West View High School is comparing T-shirt companies where they can purchase their practice shirts. The t
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This problem has several items. So, let's solve it step by step.
1. Compare the graphs of the logarithmic functions f(x)=log7x and g(x)=log4x.
In the Figure below, we have tha graph of the two functions. The graph in red is and the graph in blue is
. The x-intercept of
is:
On the other hand, the x-intercept of is:
Each graph begins in the fourth quadrant and is increasing quickly. As the graph crosses the x-axis at each x-intercept, each graph does not increase as fast. The graph continues to increase slowly throughout the first quadrant.
2. For what values of x is f=g
We can find this answer by taking this equation:
As you can see this is an absurd result since 7 is not equal to 4. The conclusion is that the function is always different from
, that is,
3. For what values f>g
From the graph, we can see that the red function is always greater than the blue function. Therefore,
