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3 years ago

Which logarithmic equation is equivalent to this exponential equation? 12=5^x

Mathematics

1 answer:

Brut [27]3 years ago

5 0

Given:

The equation is:

$12=5^x$

To find:

The logarithmic equation that is equivalent to the given exponential equation.

Solution:

According to the property of logarithm:

$a=b^x\Leftrightarrow \log_b a=x$

We have,

$12=5^x$

Here, $a=12,b=5$ . By using the above property of logarithm, we get

$\log_{5}12=x$

$x=\log_{5}12$

Therefore, the correct option is C.

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Mia did a study for a health class about the effects of the length of a person's foot and their shoe size. Based on a graph of h

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Answer: The answer is A.

Step-by-step explanation: The only valid conclusion that is listed in the options is choice A. The correct one is that the length of a person’s foot is a cause of their shoe size, which implies that there is also a correlation between the length of a person’s foot and their shoe size.

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3 years ago

Pls answer correctly I’ll give you brainliest

Montano1993 [528]

The answer is 0, as there is no slope going up or down.

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3 years ago

Find the eighth term of the

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Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

$a_{n}$ = a₁ $(r)^{n-1}$

where a₁ is the first term and r the common ratio, hence

$a_{8}$ = 6 × $(-1/3)^{7}$ = 6 × - $\frac{1}{3^{7} }$ = 6 × - $\frac{1}{2187}$ = - $\frac{2}{729}$

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3 years ago

Determine the most precise name for ABCD (parallelogram, rhombus, rectangle, or square). Explain how you determined your answer.

Sonja [21]

<h3>Answer: Rhombus</h3>

======================================================

Reason:

Let's find the distance from A to B. This is equivalent to finding the length of segment AB. I'll use the distance formula.

$A = (x_1,y_1) = (3,5) \text{ and } B = (x_2, y_2) = (7,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-7)^2 + (5-6)^2}\\\\d = \sqrt{(-4)^2 + (-1)^2}\\\\d = \sqrt{16 + 1}\\\\d = \sqrt{17}\\\\d \approx 4.1231\\\\$

Segment AB is exactly $\sqrt{17}$ units long, which is approximately 4.1231 units.

If you were to repeat similar steps for the other sides (BC, CD and AD) you should find that all four sides are the same length. Because of this fact, we have a rhombus.

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

Let's see if this rhombus is a square or not. We'll need to see if the adjacent sides are perpendicular. For that we'll need the slope.

Let's find the slope of AB.

$A = (x_1,y_1) = (3,5) \text{ and } B = (x_2,y_2) = (7,6)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{6 - 5}{7 - 3}\\\\m = \frac{1}{4}\\\\$

Segment AB has a slope of 1/4.

Do the same for BC

$B = (x_1,y_1) = (7,6) \text{ and } C = (x_2,y_2) = (6,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 6}{6 - 7}\\\\m = \frac{-4}{-1}\\\\m = 4\\\\$

Unfortunately the two slopes of 1/4 and 4 are not negative reciprocals of one another. One slope has to be negative while the other is positive, if we wanted perpendicular lines. Also recall that perpendicular slopes must multiply to -1.

We don't have perpendicular lines, so the interior angles are not 90 degrees each.

Therefore, this figure is not a rectangle and by extension it's not a square either.

The best description for this figure is a <u>rhombus</u>.

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2 years ago

Read 2 more answers

Does the quadratic function

const2013 [10]

Answer:

[0] real zeros

Step-by-step explanation:

You can use the discriminant of the quadratic formula which is b² – 4ac to determine the # of real zeros by knowing that:

2 real zero(s) occur when b² – 4ac > 0.
1 real zero(s) occur when b² – 4ac = 0.
0 real zero(s) occur when b² – 4ac < 0.

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3 years ago