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thinking problem 5 determine the points of intersection for the graph y equals to 2 times 3 to the power of x and y equals to 6 times 2 to the power of x round your answer to one decimal place ok so when we say a point of intersection that means the Y values will be seen for both these graphs at that point right so x and y values have to be same that is what it is so lets equate both the Y values so we get 2 times 3 3 to the power of X should be close to 6 times 2 to the power of X clay so that is how we can start solving this problem right now you can divide 6 by 2 and you get 3 to the power of x equals 2/3 times 2 to the power of X okay and now this is a critical stage lets divide by 3 so what do you get the 3 to the power of X divided by 3 is equals to 2 to the power of X correct now this is 3 to the power of X divided by 3 can be written as 3 to the power of X minus 1 which is equals to 2 to the power of X correct so that is how we can write them as exponents right and now to so