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2 years ago

Simplify the following expression. log(9x^5) + 5 log (1/x)

Mathematics

1 answer:

Darya [45]2 years ago

6 0

Answer:

log9

Step-by-step explanation:

hello :

note : a>0 and b>0

1) log(ab) = loga+logb

2) loga^n = nloga.....n in N

log(9x^5) + 5 log (1/x) = log(9x^5) + log (1/x)^5 = log((9x^5) (1/x)^5)

= log(9x^5)/(x^5)) = log9 because : (1/x)^5 = 1/x^5

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Mr. Smith is purchasing a $ 100000 house. The down payment is 20 % of the price of the house. He is given the choice of two mort

notka56 [123]

<h2>Answer:</h2>

The price of the house = $ 100000

The down payment is 20 % of 100000 means $0.20\times100000=20000$ dollars

So, loan amount will be = $100000-20000=80000$ dollars

30-year mortgage at a rate of 7 %

p = 80000

r = $7/12/100=0.005833$

n = $30\times12=360$

EMI formula is :

$\frac{p\times r\times(1+r)^n}{(1+r)^n-1}$

Putting the values in formula we get;

$\frac{80000\times0.005833\times(1+0.005833)^360}{(1+0.005833)^360-1}$

= $\frac{80000\times0.005833\times(1.005833)^360}{(1.005833)^360-1}$

Monthly payment = $532.22

So, total amount paid in 30 years will be = $532.22\times360=191599.20$

Interest paid will be = $191599.20-100000=91599.20$ dollars

15-year mortgage at a rate of 7 %.

Here everything will be same as above. Only n will change.

n = $15\times12=180$

Putting the values in formula we get;

$\frac{80000\times0.005833\times(1+0.005833)^180}{(1+0.005833)^180-1}$

= $\frac{80000\times0.005833\times(1.005833)^180}{(1.005833)^180-1}$

Monthly payment = $719.04

Total amount paid in 15 years will be = $719.04\times180=129427.20$

Interest paid will be = $129427.20-100000=29427.20$ dollars

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2 years ago

The area of the circle is 78.5 units. What is the radius? Use 3.14 for pi.

irga5000 [103]

The radius is 5
5 x 5 = 25
25 x 3.14 = 78.5

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2 years ago

How many solutions can be found for the equation −4x − 11 = 2(x − 3x) + 13?

nignag [31]

Answer:

None

Step-by-step explanation:

-4x-11=2(x-3x)+13

-4x-11=2x-6x+13

-4x-11=-4x+13

-11=13

Therefore, there are no solutions for the equation as both sides will never be equal to each other.

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2 years ago

A rectangle is divided into 8 equal parts. Two parts are shaded. Which fraction is equivalent to the shaded area of the rectangl

Maslowich

If the shaded area is 2 out of the 8 equal parts, the fraction is 2/8, which simplifies to 1/4.

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3 years ago

Read 2 more answers

Solve the system of equations. y = -5x + 24 y = 4x - 21 a. ( -5, -1) c. ( -1, 5) b. ( 5, -1) d. No solution

Svetlanka [38]

y = -5x + 24

y = 4x - 21

Since both of these equations are equal to Y, theyre equal to each other.

So we can make an equation with y = -5x + 24 in one side and y = 4x - 21 on the other.

-5x + 24 = 4x - 21

Now in order to get the value of x we need to isolate it in one side of the equation. We can do this by subtracting 24 from both sides of the equation:

-5x + 24 - 24 = 4x - 21 - 24

-5x = 4x - 45

Now we subtract 4x from both sides so the 4x shift to the other side

-5x - 4x = 4x - 4x - 45

-9x = -45

Finally divide both sides by -9 so x is by itself

(-9)÷(-9x) = -(45)÷(-9)

x = 5

Since we did all of this to BOTH sides of the equation, both sides are still equal to each other and the equation still is true.

Now apply x = 5 to either of the initial equations to find the value of Y

y = -5x + 24 or y = 4x - 21

(I'll do both but u only need one)

y = -5(5) + 24

y = -25 + 24

y = -1

y = 4(5) - 21

y = 20 - 21

y = -1

Either way, X is 5 and Y is -1

Answer (5, -1)

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2 years ago