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seropon [69]
2 years ago
13

I need help with pre calculus.

Mathematics
1 answer:
Nata [24]2 years ago
5 0

Answer:

  h(x) = 4·log₃(x) +2

Step-by-step explanation:

<h3>Part A:</h3>

  h(x) = f(x) +g(x)

  h(x) = (log₃(x) +3) +(log₃(x³) -1)

  h(x) = log₃(x) +3·log₃(x) +2

  h(x) = 4·log₃(x) +2 . . . . . "simplest" form

  h(x) = log₃(9x⁴) . . . . . . . as a single logarithm

__

<h3>Part B:</h3>

No system of equations is given. Perhaps you want to find x for f(x) = g(x).

  log₃(x) +3 = log₃(x³) -1

  log₃(x) +3 = 3·log₃(x) -1

  4 = 2·log₃(x) . . . . . . . . . . . add 1-log₃(x)

  2 = log₃(x) . . . . . . . . . . . . divide by 2

  3² = x = 9 . . . . . . . . . . . . . take the antilog

The solution to f(x) = g(x) is x = 9.

_____

<em>Additional comment</em>

The relevant rules of logarithms are ...

  a = log₃(b)   ⇔   3^a = b

  log(a^b) = b·log(a)

  log(ab) = log(a) +log(b)

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Monica [59]

Answer:

1)

\text{ Slope = -3}

2)

y+4=-\frac{7}{8}(x-7)

3)

y=-\frac{7}{8}x+\frac{17}{8}

Step-by-step explanation:

We want to write the equation of the line that passes through the points (7, -4) and (-1, 3) first in point-slope form and then in slope-intercept form.

1)

First and foremost, we will need to find the slope of the line. So, we can use the slope-formula:

m=\frac{y_2-y_1}{x_2-x_1}

Let (7, -4) be (x₁, y₁) and let (-1, 3) be (x₂, y₂). Substitute them into our slope formula. This yields:

m=\frac{3-(-4)}{-1-7}

Subtract. So, our slope is:

m=\frac{7}{-8}=-7/8

2)

Now, let's use the point-slope form:

y-y_1=m(x-x_1)

We will substitute -7/8 for our slope m. We will also use the point (7, -4) and this will be our (x₁, y₁). So, substituting these values yield:

y-(-4)=-\frac{7}{8}(x-7)

Simplify. So, our point-slope equation is:

y+4=-\frac{7}{8}(x-7)

3)

Finally, we want to convert this into slope-intercept form. So, let's solve for our y.

On the right, distribute:

y+4=-\frac{7}{8}x+\frac{49}{8}

Subtract 4 from both sides. Note that we can write 4 using a common denominator of 8, so 4 is 32/8. This yields:

y=-\frac{7}{8}x+\frac{49}{8}-\frac{32}{8}

Subtract. So, our slope-intercept equation is:

y=-\frac{7}{8}x+\frac{17}{8}

And we're done!

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