At what point do the graphs of y=log5 x and y= log0.5 x intersect?
The graphs of y = log5 x and y = log0.5 x intersect when the two functions are equal to each other. In other words, they intersect at the points where log5 x = log0.5 x.
To solve for x in this equation, we can first rewrite it using the properties of logarithms:
log5 x = log0.5 x
log(x) / log(5) = log(x) / log(0.5)
Since the log base is the same (both are natural logs), we can cancel them out:
log(x) = log(x)
This means that the graphs of y = log5 x and y = log0.5 x intersect for all values of x. In other words, the graphs are the same and overlap each other.