Phillip is using logarithms to solve the equation 6^3x = 18. Which of the following equations would be equivalent to his origina
2 answers:
Answer: 3x log 6 = log 18
Step-by-step explanation:
Here, the given equation is,
Which is an exponential equation,
Generally, for solving an exponential expression, we take log for eliminating variable from the power.
Also, When we take any change in both sides of an expression then the new expression is equivalent to the expression.
By taking log on both side in the above,
( since,
)
Which is the required equivalent expression.
⇒ Fourth option is correct.
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Hello!
The directrix of a parabola is a fixed line used in describing a curve or surface.
The standard form a parabola is 4p(x - h) = (y - k)². In this equation, h, k is the vertex, and p is the focal point.
To find the standard form, first, we would find p.
Since the equation given, y² = -24x, has a vertex at (0, 0), h, k would be zero. In this case, we can find p now.
4p = -24 (divide both sides by 4)
p = -6
4(-6)(x - 0) = (y - 0)² which can be simplified to: 4(-6)(x) = y².
Looking at the graph of the parabola, it is symmetric around the x-axis, so therefore, the directrix is a line parallel to the y-axis. To find the directrix, use the formula: x = 0 - p, and we know that p = -6.
x = 0 - (-6)
x = 6
Therefore, the directrix of the parabola is choice D, x = 6.
