Which equation has x=-6 as the solution? A-logx36=2. B-log3(2x-9)=3. C-log3 216=x. D-log3(-2x-3)=2
1 answer:
I posted this to your other question as well:
So we have:
A)
B)
C)
D)
We need to try x = –6 in each equation until we find a solution that makes both sides of the equation equal.
For A, this gives an undefined result. Logarithms are only defined for bases that are positive real numbers not equal to 1.
For B, this again gives an undefined result. The logarithm of a number is only defined when that number is a positive real number. It would be –21, which is undefined.
For C, we have a defined operation, but
.
Finally, for D, we have
This is true.
So we have:
A)
B)
C)
D)
We need to try x = –6 in each equation until we find a solution that makes both sides of the equation equal.
For A, this gives an undefined result. Logarithms are only defined for bases that are positive real numbers not equal to 1.
For B, this again gives an undefined result. The logarithm of a number is only defined when that number is a positive real number. It would be –21, which is undefined.
For C, we have a defined operation, but
Finally, for D, we have
This is true.
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Since g(6)=6, and both functions are continuous, we have:
![\lim_{x \to 6} [3f(x)+f(x)g(x)] = 45\\\\\lim_{x \to 6} [3f(x)+6f(x)] = 45\\\\lim_{x \to 6} [9f(x)] = 45\\\\9\cdot lim_{x \to 6} f(x) = 45\\\\lim_{x \to 6} f(x)=5](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%206%7D%20%5B3f%28x%29%2Bf%28x%29g%28x%29%5D%20%3D%2045%5C%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20%5B3f%28x%29%2B6f%28x%29%5D%20%3D%2045%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20%5B9f%28x%29%5D%20%3D%2045%5C%5C%5C%5C9%5Ccdot%20lim_%7Bx%20%5Cto%206%7D%20f%28x%29%20%3D%2045%5C%5C%5C%5Clim_%7Bx%20%5Cto%206%7D%20f%28x%29%3D5)
if a function is continuous at a point c, then
,
that is, in a c ∈ a continuous interval, f(c) and the limit of f as x approaches c are the same.
Thus, since
, f(6) = 5
Answer: 5
if a function is continuous at a point c, then
that is, in a c ∈ a continuous interval, f(c) and the limit of f as x approaches c are the same.
Thus, since
Answer: 5