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blsea [12.9K]
3 years ago
11

Rewrite the form In exponential form: Log100 = x

Mathematics
1 answer:
andrey2020 [161]3 years ago
6 0

Answer:

10^x=100

Step-by-step explanation:

You know how subtraction is the <em>opposite of addition </em>and division is the <em>opposite of multiplication</em>? A logarithm is the <em>opposite of an exponent</em>. You know how you can rewrite the equation 3 + 2 = 5 as 5 - 3 = 2, or the equation 3 × 2 = 6 as 6 ÷ 3 = 2? This is really useful when one of those numbers on the left is unknown. 3 + _ = 8 can be rewritten as 8 - 3 = _, 4 × _ = 12 can be rewritten as 12 ÷ 4 = _. We get all our knowns on one side and our unknown by itself on the other, and the rest is computation.

We know that 3^2=9; as a logarithm, the <em>exponent</em> gets moved to its own side of the equation, and we write the equation like this: \log_3{9}=2, which you read as "the logarithm base 3 of 9 is 2." You could also read it as "the power you need to raise 3 to to get 9 is 2."

One historical quirk: because we use the decimal system, it's assumed that an expression like \log1000 uses <em>base 10</em>, and you'd interpret it as "What power do I raise 10 to to get 1000?"

The expression \log100=x means "the power you need to raise 10 to to get 100 is x," or, rearranging: "10 to the x is equal to 100," which in symbols is 10^x=100.

(If we wanted to, we could also solve this: 10^2=100, so \log100=2)

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Which of the following estimates at a 95% confidence level most likely comes form a small sample?
KonstantinChe [14]

OptionAStep-by-step explanation:95% confidence interval is obtained using the following formulaCOnfidence interval lower bound = mean - critical value * sigma/sq rt nand upper bound = mean + critical value*sigma/sq rt nThus margin of error = critical value*sigma/rt nvaries indirectly as n provided others are remaining the same.Hence lower sample indicates higher margin of errorOut of 4 options given we find that 1 option has maximum margin of error as 21%Hence option. A is most likely coming from a small sample.

6 0
2 years ago
The length of a rectangle is 3 inches more than the width. The area is 10 square inches. Find the dimensions
mr_godi [17]

Answer:

Width = 2

Length = 5

Step-by-step explanation:

let A be the area of the rectangle

   L be the length of the rectangle

   w be the width of the rectangle

<u><em>Formula</em></u>: ‘<u><em>area of a rectangle</em></u>’

A = L × w

…………………………………………………

A = L × w

⇔ 10 = (w + 3) × w

⇔ 10 = w² + 3w

⇔ w² + 3w - 10 = 0  

<u><em>Solving the quadratic equation</em></u> w² + 3w - 10 =  0 :

Δ = 3² - 4(1)(-10) = 9 - (-40) = 9 + 40 = 49

then √Δ = 7

\Longrightarrow w=\frac{-b+\sqrt{\Delta } }{2a} =\frac{-3+7}{2} =2

  or\ w=\frac{-b-\sqrt{\Delta } }{2a} =\frac{-3-7}{2} =-5

-5 is not valid ,because w represents the width

which must be a positive number

Then  w = 2

<u><em>Conclusion</em></u>:

Width = 2

Length = 2 + 3 = 5

6 0
2 years ago
A vehicle arriving at an intersection can turn right, turn left, or continue straight ahead. The experiment consists of observin
Temka [501]

Answer:

a) Sample space (S) = {TR, TL, Cs}

b) Pr(Vehicle Turns) = 2/3.

Step-by-step explanation:

a) By sample space (S) we mean the list all possible outcome of an event. From the illustration in the question, only three (3) outcome is possible:

i) Vehicle Turn Right (TR)

ii) Vehicle Turn Left (TL)

iii) Continue Straight ahead (Cs)

And since the experiment consists of observing the movement of a single vehicle through the intersection, then, the sample space (S) is:

==> {TR, TL, Cs}

b) Since we are assuming that all sample points are equally likely, it imply that they have equal probability of occurring. And by probability:

Pr(TR) = 1/3

Pr(TL) = 1/3

Pr(Cs) = 1/3

Meanwhile, the question wants us to find the probability that the vehicle turns. This means, the vehicle turning either right or left. Thus;

Pr(vehicle turns) = Pr(TR) or Pr(TL) = Pr(TR) + Pr(TL)

Pr(vehicle turns) = (1/3) + (1/3) = 2/3

4 0
3 years ago
The function f(x) = 5()x is reflected over the y-axis. Which equations represent the reflected function? Check all that apply.
Taya2010 [7]
Key term "Reflected", which is equivalent to "inverse". This means that the graph, although remains with the same points, is "reflected". Think of a mirror. 
Say y = m(x). The reflected result is y = -m(x). Or in another case, y = m(-x) will be reflected to y = m(x). 
Lets break this rule further. Say your point was (a,b) which is code for (x,y). If we're looking at the x-axis, the y becomes negative. Henceforth, it becomes (x,-y) and vice versa. 
In this case, we're looking at the y-axis reflected, meaning, the x-value will be NEGATIVE. 

Answer is C: m(x) - 5() -x This can be seen as m(x) = m(-x) as well.
3 0
3 years ago
Read 2 more answers
Which inequality represents the situation ten less than a number is a minimum of 30?
Shkiper50 [21]

Answer:

x - 10 ≥ 30

Step-by-step explanation:

I'm 99.8% sure

It says 10 less than a number so that means subtract 10 from a number

Then it says minimum of 30 so that means the number has to be 30 or more so that's why I use the more than of equal to sign.

Hope this helps!

6 0
3 years ago
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