Eric Nicholas K's answer to Candice lim's Secondary 3 A Maths Singapore question.
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Candice, the graphs reflected on the diagram are as follows.
Red - y = log (to base 3) x
Blue - y = 2x - 1
Apparently the graphs do not intersect at all, meaning to say that the equation 9^x = 3x has no real roots at all.
To confirm this, I plot another graph y = 9^x - 3x to see if this graph intersects the x-axis or not (in green). If the graph intersects the x-axis, yes there is a solution to the equation 9^x - 3x = 0 (and hence there is a solution to the equation 9^x = 3x). Apparently, the non-intersection with the x-axis confirms my first set of two graphs above.
Red - y = log (to base 3) x
Blue - y = 2x - 1
Apparently the graphs do not intersect at all, meaning to say that the equation 9^x = 3x has no real roots at all.
To confirm this, I plot another graph y = 9^x - 3x to see if this graph intersects the x-axis or not (in green). If the graph intersects the x-axis, yes there is a solution to the equation 9^x - 3x = 0 (and hence there is a solution to the equation 9^x = 3x). Apparently, the non-intersection with the x-axis confirms my first set of two graphs above.
Date Posted:
4 years ago
I see...many thanks, Mr Eric. Have a good day ahead :)
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