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sergeinik [125]
2 years ago
6

Please help! The answer to this is 2 but I don't know how to actually solve it so can someone please show the work for this?

Mathematics
2 answers:
s344n2d4d5 [400]2 years ago
4 0

Answer:

2

Step-by-step explanation:

basically logarithms are like reverse exponents

log7, 49 is basically asking 7 to the what gets you 49

because of that its 2 because 7^2 gets you 49

svetoff [14.1K]2 years ago
3 0
<h3>Answer:    2</h3>

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

Explanation:

Recall that any exponential equation of the form b^x = y can be written into its equivalent log form of \log_{b}(y) = x. Note how in both cases, 'b' is the base. For the exponential equation, x is buried in the exponent and y is free on its own. In the log equation, we have y buried in the log and x is free or isolated on its own.

In your case, we have b = 7 and y = 49. This means \log_{7}(49) = x is the same as 7^x = 49 when converting from log form to exponential form. Then we can rewrite that 49 into 7^2 to get 7^x = 7^2. The bases are both 7, so the exponents must be the same as well. Therefore, x = 2.

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

We could follow a different approach. We could apply the change of base formula. The change of base formula is

\log_{b}(x) = \frac{\log(x)}{\log(b)}

On the left side, we have log base b; however, on the right side, the log can be any base we want. Oftentimes it's handy to go with base 10, though again it doesn't matter the base on the right hand side logs.

So we would then say...

\log_{b}(x) = \frac{\log(x)}{\log(b)}\\\\\log_{7}(49) = \frac{\log(49)}{\log(7)}\\\\\log_{7}(49) = \frac{1.69019608002851}{0.84509804001426}\\\\\log_{7}(49) = 1.99999999999999\\\\

Due to rounding error, we don't land exactly on 2 as expected. However, we get close enough.

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Twice a number is equal to 35 more than seven times the number. Find the number
amm1812

number - n

Twice a number - 2n

Seven times the number - 7n


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5n = -35

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Check:

2(-7) = 7(-7) +35

-14 = -49 + 35

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3 years ago
Suppose a certain computer virus can enter a system through an email or through a webpage. There is a 40% chance of receiving th
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Answer:

P = 0.42

Step-by-step explanation:

This probability problem can be solved by building a Venn like diagram for each probability.

I say that we have two sets:

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-Set B, that is the probability of receiving it through the webpage.

The most important information in these kind of problems is the intersection. That is, that he virus enters the system simultaneously by both email and webpage with a probability of 0.17. It means that A \cap B = 0.17.

By email only

The problem states that there is a 40 chance of receiving it through the email. It means that we have the following equation:

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A + 0.17 = 0.40

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The problem states that there is a 40% chance of receiving it through the email. 23% just through email and 17% by both the email and the webpage.

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There is a 35% chance of receiving it through the webpage. With this information, we have the following equation:

B + (A \cap B) = 0.35

B + 0.17 = 0.35

B = 0.18

where B is the probability that the system receives the virus just through the webpage.

The problem states that there is a 35% chance of receiving it through the webpage. 18% just through the webpage and 17% by both the email and the webpage.

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P + 0.23 + 0.18 + 0.17 = 1

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P = 0.42

There is a probability of 42% that the virus does not enter the system at all.

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3 years ago
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Step-by-step explanation:

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