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3 years ago

Which logarithmic equation is equivalent to the exponential equation below?

Mathematics

2 answers:

jek_recluse [69]3 years ago

7 0

The answer is B.
ln both sides to clear the 'e' and bring 'a' out of the power.

Fed [463]3 years ago

5 0

Answer:

B. $\ln 87.18=a$

Step-by-step explanation:

We are given,

The logarithmic equation is $87.18=e^a$ .

Taking log with base 'e' on both sides, we get,

$87.18=e^a$

i.e. $\log_{e}87.18=\log_{e}e^a$ ............( $\log x^y=y\log x$ )

i.e. $\log_{e}87.18=a\log_{e}e$ ............( $\log_{a}a=1$

i.e. $\log_{e}87.18=a$

Thus, option B is correct.

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What is the solution to w - 9 1/2 = 15<br>24 1/2<br>6 1/2<br>23 1/2<br>5 1/2

VladimirAG [237]

Answer:

Option A

Step-by-step explanation:

Convert mixed fraction to improper fraction.

$\sf w - 9\dfrac{1}{2}=15\\\\ w - \dfrac{19}{2}=15$

Now isolate 'w'

$\sf w = 15 +\dfrac{19}{2}\\\\= \dfrac{15*2}{1*2}+\dfrac{19}{2}\\\\=\dfrac{30}{2}+\dfrac{19}{2}\\\\=\dfrac{30+19}{2}\\\\=\dfrac{49}{2}\\\\= 24\dfrac{1}{2}$

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2 years ago

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3 years ago

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Simplify- 5+2{3x+7(2-x)}

oksano4ka [1.4K]

Answer:

16x+19

Step-by-step explanation:

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4 0

3 years ago

Describe the behavior of the function ppp around its vertical asymptote at x=-2x=−2x, equals, minus, 2.

insens350 [35]

Answer:

$x->-2^{-}, p(x)->-\infty$ and as $x->-2^{+}, p(x)->-\infty$

Step-by-step explanation:

Given

$p(x) = \frac{x^2-2x-3}{x+2}$ -- Missing from the question

Required

The behavior of the function around its vertical asymptote at $x = -2$

$p(x) = \frac{x^2-2x-3}{x+2}$

Expand the numerator

$p(x) = \frac{x^2 + x -3x - 3}{x+2}$

Factorize

$p(x) = \frac{x(x + 1) -3(x + 1)}{x+2}$

Factor out x + 1

$p(x) = \frac{(x -3)(x + 1)}{x+2}$

We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)

We are only interested in the sign of the result

----------------------------------------------------------------------------------------------------------

As x approaches -2 implies that:

$x -> -2^{-}$ Say x = -3

$p(x) = \frac{(x -3)(x + 1)}{x+2}$

$p(-3) = \frac{(-3-3)(-3+1)}{-3+2} = \frac{-6 * -2}{-1} = \frac{+12}{-1} = -12$

We have a negative value (-12); This will be called negative infinity

This implies that as x approaches -2, p(x) approaches negative infinity

$x->-2^{-}, p(x)->-\infty$

Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)

As x leaves -2 implies that: $x>-2$

Say x = -2.1

$p(-2.1) = \frac{(-2.1-3)(-2.1+1)}{-2.1+2} = \frac{-5.1 * -1.1}{-0.1} = \frac{+5.61}{-0.1} = -56.1$

We have a negative value (-56.1); This will be called negative infinity

This implies that as x leaves -2, p(x) approaches negative infinity

$x->-2^{+}, p(x)->-\infty$

So, the behavior is:

$x->-2^{-}, p(x)->-\infty$ and as $x->-2^{+}, p(x)->-\infty$

6 0

3 years ago

Rosey purchased 364 flowers to make centerpieces for a party. There are 13 tables. Each table will have 4 vases with the same nu

Olin [163]

7. honestly not 100% sure. i did 364 divided by 13 which was 28 so 28 flowers per table. and then 28 divided by 4. 7 flowers per vase.

8 0

2 years ago