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Andru [333]
2 years ago
6

Find the inverse of y=ln2x

Mathematics
1 answer:
never [62]2 years ago
4 0

Answer:

The exponential function, exp : R → (0,∞), is the inverse of the natural logarithm, that is, exp(x) = y ⇔ x = ln(y). Remark: Since ln(1) = 0, then exp(0) = 1. Since ln(e) = 1, then exp(1) = e.

Step-by-step explanation:The exponential function, exp : R → (0,∞), is the inverse of the natural logarithm, that is, exp(x) = y ⇔ x = ln(y). Remark: Since ln(1) = 0, then exp(0) = 1. Since ln(e) = 1, then exp(1) = e.

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I need explanations for Mathematical Proofs.
erma4kov [3.2K]

Answer:

Proofs employ logic expressed in mathematical symbols, along with natural language which usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic.

According to Bleiler-Baxter & Pair [22], for a mathematician, a proof serves to convince or justify that a certain statement is true. But it also helps to increase the understanding of the result and the related concepts. That is why a proof also has the role of explanation.

There are many different ways to go about proving something, we'll discuss 3 methods: direct proof, proof by contradiction, proof by induction. We'll talk about what each of these proofs are, when and how they're used. Before diving in, we'll need to explain some terminology.

Although I will focus on proofs in mathematical education per the topic of the question, first and foremost proofs are so hard because they involve taking a hypothesis and attempting to prove or disprove it by finding a counterexample. There are many such hypotheses that have (had) serious monetary rewards available.

In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference.

All mathematicians in the study considered proofs valuable for students because they offer students new methods, important concepts and exercise in logical reasoning needed in problem solving. The study shows that some mathematicians consider proving and problem solving almost as the same kind of activities.

More information for you..

https://youtu.be/V5tUc-J124s

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3 0
3 years ago
Last year , there were 30 male members and 20 female members in a Chess Club . This year , the number of male members is decreas
LekaFEV [45]

The r% of a quantity x is computed by dividing x in 100 parts, and considering r of such parts. So, the r% of the male is

30\times\cfrac{r}{100} = 0.3 r

and similarly, the r% of female is

20\times\cfrac{r}{100} = 0.2 r

The number of males decreased by this quantity, so now it is

30 - 0.3r

and the number of female increased by this quantity, so now it is

20+0.2r

we know that these two new counts are the same number, so we can build and solve the equality

30 - 0.3r = 20+0.2r

Subtract 20 and add 0.3r from both sides:

10 = 0.5r

Divide both sides by 0.5 to solve for r:

r = 20

Let's check the answer

The 20% of 30 is 30 \times \frac{20}{100} = 6, while the 20% of 20 is 4. So, we are stating that 30-6 = 20+4 which is true because both expressions evaluate to 24.

7 0
3 years ago
What is the length of line segment KJ?
Karolina [17]

Please consider the attached file.

We can see that triangle JKM is a right triangle, with right angle at M. Segment KM is 6 units and segment MJ is 3 units. We can also see that KJ is hypotenuse of right triangle.

We will use Pythagoras theorem to solve for KJ as:

KJ^2=KM^2+MJ^2

KJ^2=6^2+3^2

KJ^2=36+9

KJ^2=45

Now we will take positive square root on both sides:

\sqrt{KJ^2}=\sqrt{45}

KJ=\sqrt{9\cdot 5}

KJ=3\sqrt{5}

Therefore, the length of line segment KJ is 3\sqrt{5} and option D is the correct choice.

5 0
3 years ago
What is the solution of 5y + 1=31
gayaneshka [121]

Answer:

y=6

Step-by-step explanation:

edge2020

4 0
2 years ago
Read 2 more answers
What is the answer i'm having trouble :( click the picture
Vikentia [17]

Step-by-step explanation:

So 2 pints = 1 quart

She need 3 quart

so 2 pints × 3 = 1 quart × 3

6 pints = 3 quart

...

The she need 6 pints which is

2 cups = 1 pint

She need 6, so mutiply with 6

2 cups × 6 = 1 pint × 6

12 cups = 6 pints

Then this is the answer, you got

12 cups = 6 pints = 3 quart

She need 12 cups of water to make fruit punch

5 0
2 years ago
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