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Gennadij [26K]
3 years ago
14

Use the definition of logarithm to simplify each expression.

Mathematics
1 answer:
konstantin123 [22]3 years ago
7 0
1)\ \ \ log 10 ^{10}=x\ \ \ \Leftrightarrow\ \ \ 10^x=10^{10}\ \ \ \Leftrightarrow\ \ \ \ \ \ x=10\\\\2) \ \ \ log 10 ^{100}=x\ \ \ \Leftrightarrow\ \ \ 10^x=10^{100}\ \ \ \Leftrightarrow\ \ \ x=100\\ \\ 3)\ \ \ log 10 ^ {10-4}=x\ \ \ \Leftrightarrow\ \ \ 10^x=10^{10-4}\ \ \ \Leftrightarrow\ \ \ x=6
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Can someone please explain to me how I do this?
Nastasia [14]

Answer:

x = 12.77 cm

Step-by-step explanation:

In this problem, we will use trigonometry to find the missing value. I will use the 70 degree angle to find it.

12cm is the opposite value for 70, and x is the hypotenuse. We will use Sine to solve this problem.

Since we are missing the hypotenuse, we set up the equation like this -

x = 12/Sin(70)

This leads us to our answer, x=12.77 cm (rounded)

6 0
3 years ago
Read 2 more answers
Please help me with this question :)
Basile [38]
Algebraic Equation:
1/2p = 150
Solution:
150 ÷ 1/2 = 300
p = $300
The original price was $300
7 0
2 years ago
How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters? We want 95% confidence that
lukranit [14]

Answer: 25 computers will be selected

Step-by-step explanation:

Where: Z -value at 95% confidence = 1.96; SD = Standard deviation = 10 minutes; N = Sample size; Margin error = 4 minutesSubstituting;4 = 1.96*10/Sqrt (N)Sqrt (N) = (1.96*10)/4 = 4.9N = 4.9^2 = 24.01 ≈ 25

5 0
2 years ago
Simplify the following expression.<br> -14x^2+9x-4x^2+5
Naya [18.7K]

Answer:

i think the answer is -18x^(2)+9x+5

-18x^(2)+9x+5

Subtract 4x^2 from  −14x^2

3 0
3 years ago
A bag contains 3 red,4 green, and 5 blue marbles. Three marbles are drawn at random. What is the probability that all three are
Reptile [31]

Answer:

1/22

Step-by-step explanation:

assuming that the marbles drawn are not replaced:

P(red) = 3/12 or 1/4

P(green) = 4/11

P(blue) = 5/10 or 1/2

multiply the probabilities together:

1/4 x 4/11 x 1/2 = 1/22

8 0
2 years ago
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