The graphs of f(x)=−5/3x+9 and g(x)=2^x−1 intersect at (3, 4) .
What is the solution of −5/3x+9=2^x−1 ?
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They do not intersect at (3,4)
(3,4) does not satisfy g(x) = 2^x - 1
RS = 2^3 - 1 = 7
LS = 4, no good
(3,4) work in f(x) = -5/3x + 9
RS = -5/3(3) + 9
= 4
So it does work in the other equation.
did you mean g(x) = 2^(x-1) ??
RS = 2^2 = 4 = RS
you must have meant that!
so clearly the solution to
-5/3x + 9 = 2^(x-1) is x = 3
To solve the equation −5/3x+9=2^x−1, we can set the two equations equal to each other, since they intersect at (3, 4):
−5/3x + 9 = 2^x - 1
To proceed further, we can simplify the equation by multiplying through by 3 to eliminate the denominator:
-5x + 27 = 3(2^x) - 3
Next, we can move all terms to one side of the equation:
-5x - 3(2^x) = -30 + 3
Simplifying, we have:
-5x - 3(2^x) = -27
At this point, finding the exact solution analytically is not straightforward. However, we can use numerical methods or approximate solutions.
To solve the equation −5/3x+9=2^x−1, we need to find the value of x that makes the equation true.
One method to solve this equation is by graphing both functions f(x) = −5/3x + 9 and g(x) = 2^x − 1. The point of intersection of the two graphs represents the solution to the equation.
Given that the graphs intersect at (3, 4), we know that when x = 3, both f(x) and g(x) have the same y-value, which is 4.
Now let's substitute x = 3 into both equations and see if we get the same y-value:
For f(x): f(3) = −5/3(3) + 9 = -5 + 9 = 4
For g(x): g(3) = 2^3 − 1 = 8 − 1 = 7
As we can see, the y-values are not the same when x = 3. Therefore, (3, 4) cannot be the solution to the equation −5/3x + 9 = 2^x − 1.
Hence, there is no solution to the equation −5/3x + 9 = 2^x − 1.