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2 years ago

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:

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

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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Please I need help!

Monica [59]

Answer:

$\text{ Slope = -3}$

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

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

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.

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:

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

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:

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

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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3 years ago

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Answer:

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