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2 years ago

Use the properties of logarithms to prove log81000= log210.

Mathematics

1 answer:

Liula [17]2 years ago

3 0

Answer:

Step-by-step explanation:

Given the expression $log_81000 = log_210$ , to prove this expression is true using the properties of logarithm, we will follow the following steps.

Starting from the Left Hand Side:

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Suppose the radius of a circle is \color{purple}{3}3start color purple, 3, end color purple. what is its circumference?either en

Vlada [557]

$\text{Consider the circle of radius 3.}\\
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\text{we need to find the cirumference of the circle.}\\
\\
\text{we know that the circumference of the circle of radius r is given by}\\
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\text{circumference}=2\pi r\\
\\
\text{so using this formula, the circumference of the given circle is}$

$\text{Circumference}=2\pi r\\
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=2\pi \times 3\\
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=6\pi
\\
\text{so the circumference of the circle is}=6\pi\\
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\text{and in decimals, it gives}=6\times 3.14\\
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\Rightarrow \text{circumference}=18.84$

Hence the circumference of the circle is: 6π or 18.84 units

6 0

2 years ago

Read 2 more answers

Drag each expression to show whether it is equivalent to (5⋅9x)+(5⋅1), 45x+15, or 15(3x−1).

JulijaS [17]

Part A: Option e: $5(9 x+1)$

Option f: $45 x+5$

Part B: Option c: $15(3 x+1)$

Option d: $(5 \cdot 9 x)+(5 \cdot 3)$

Part C: Option a: $(5 \cdot 9 x)-(5 \cdot 3)$

Option b: $45 x-15$

Explanation:

Part A: The equation is $(5 \cdot 9 x)+(5 \cdot 1)$

Simplifying, we have,

$45x+5$

Taking the term 5 common out, we have,

$5(9 x+1)$

Thus, the above two expressions are equivalent to the equation $(5 \cdot 9 x)+(5 \cdot 1)$ .

Hence, Option e and Option f are the correct answers.

Part B: The equation is $45 x+15$

Taking the term 15 common out, we have,

$15(3 x+1)$

Also, the equation can be rewritten as,

$(5 \cdot 9 x)+(5 \cdot 3)$

Thus, the above two expressions are equivalent to the equation $45 x+15$

Hence, Option c and Option d are the correct answers.

Part C: The equation is $15(3 x-1)$

Multiplying, we have,

$45 x-15$

The above expression can be rewritten as,

$(5 \cdot 9 x)-(5 \cdot 3)$

Thus, the above two expressions are equivalent to the equation $15(3 x-1)$

Hence, Option a and Option b are the correct answers.

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2 years ago

If the following fraction is reduced, what will be the exponent on the p? -5p^5q^4/ 8p^2q^2

viktelen [127]

<span>-5p^5q^4/ 8p^2q^2
= -5p^3q^2

</span><span>exponent on the p will be 3

answer
</span><span>C.3</span>

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2 years ago

Read 2 more answers

Use the table to answer the question. House A $124,270 Annual appreciation 4% House B $114,270 Annual appreciation 5% In which o

Varvara68 [4.7K]

For the house A we have:
f (x) = 124270 (1.04) ^ x
Evaluating for 7, 8, 9 and 10 we have:
f (7) = 124270 (1.04) ^ 7 = 163530.8422
f (8) = 124270 (1.04) ^ 8 = 170072.0759
f (9) = 124270 (1.04) ^ 9 = 176874.9589
f (10) = 124270 (1.04) ^ 10 = 183949.9573

For house B we have:
f (x) = 114270 (1.05) ^ x
Evaluating for 7, 8, 9 and 10 we have:
f (7) = 114270 (1.05) ^ 7 = 160789.3653
f (8) = 114270 (1.05) ^ 8 = 168828.8336
f (9) = 114270 (1.05) ^ 9 = 177270.2752
f (10) = 114270 (1.05) ^ 10 = 186133.789

We observe that for years 7 and 8 the value of house A is greater than the value of house B.

Answer:
7 and 8

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2 years ago

Tomorrow, Mrs. Wendel's class will be using toothpicks for a science project. Each student must use at least 5 toothpicks for th

Amiraneli [1.4K]

Answer:

I'm pretty sure A but let me know if I'm wrong

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2 years ago