39. Rewrite each expression as an equivalent expression containing only one logarithm.

Mathematics

1 answer:

monitta3 years ago

3 0

Answer:

$ln{\frac{(p+q)^3}{q^2p^7} }$

Step-by-step explanation:

3 ln(p + q) − 2 ln(q) − 7 ln(p)

=ln(p+q)^3- ln(q)^2-ln(p)^7

= ln(p+q)^3-{ln(q)^2+ln(p)^7}

=ln(p+q)^3-ln(q)^2*(p)^7

=ln{ (p+q)^3÷(q)^2*(p)^7}

= $ln{\frac{(p+q)^3}{q^2p^7} }$

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Which of the following is the graph of the rational function? y=x^2+2x-8/x^2-9

rusak2 [61]

Notice that we can simplify both numerator and denominator of our rational function. In the numerator we have a quadratic expression of the form $ax^2+bx+c$ . To to simplify it, we are going to find tow numbers that add to 2 and multiply to -8; those numbers are 4 and -2.
$x^2+2x-8=(x+4)(x-2)$
In the denominator we have a difference of squares:
$x^2-9=x^2-3^2=(x+3)(x-3)$

Now we can rewrite our function:
$y= \frac{x^2+2x-8}{x^2-9} = \frac{(x+4)(x-2)}{(x+3)(x-3)}$

From the simplified form of our rational function we can infer that its graph has two vertical asymptotes at $x=3$ and $x-3$

We can conclude that the graphic of our rational function is: