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3 years ago

Use the property of logarithms to evaluate the expression. No decimals.

Mathematics

1 answer:

borishaifa [10]3 years ago

6 0

If you want to solve for x, then the answer is x = 6*sqrt(2) where "sqrt" is shorthand for "square root"

Explanation:

All logs below are base 4

log(5) - log(18) = log(20) - 2*log(x)

log(5) - log(18) = log(20) - log(x^2)

log(5/18) = log(20/x^2)

5/18 = 20/x^2 ... raise both sides as exponents (base = 4); logs cancel

5x^2 = 18*20 ... cross multiply

5x^2 = 360

x^2 = 360/5 ... divide both sides by 5

x^2 = 72

x = sqrt(72) ... see note below.

x = sqrt(36*2)

x = sqrt(36)*sqrt(2)

x = 6*sqrt(2)

note: we only consider the positive solution for x because x cannot be negative. We cannot input negative x values into log(x). The domain of log(x) is x > 0. So we don't consider "plus/minus" for the square root.

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Solve each quadratic equation. Show your work. 14. (2x – 1)(x + 7) = 0

melisa1 [442]

(2x – 1)(x + 7) = 0

2x-1=0
2x=1
x=1/2
x=0.5

x+7=0
x= -7

5 0

3 years ago

Read 2 more answers

How do I solve for x

Alchen [17]

Greetings!

To find the length of any side of a right triangle, you can use the Pythagorean Thereom. It states that the squares of two sides are equal to the square of the hypotenuse:
$a^2+b^2=c^2$

Input the information from the diagram into the formula:
$(x)^2+(x+7)^2=(13)^2$

Expand each term:
$(x)^2+(x+7)^2=(13)^2$

$x^2+((x+7)(x+7))=169$

$x^2+(x(x+7)+7(x+7))=169$

$x^2+x^2+7x+7x+49=169$

Combine like terms:
$2x^2+14x+49=169$

Add -169 to both sides:
$(2x^2+14x+49)+(-169)=(169)+(-169)$

$2x^2+14x-120=0$

Factor out the Common Term (2):
$2(x^2+7x-60)=0$

Factor the Complex Trinomial:
$2(x^2-5x+12x-60)=0$

$2(x(x-5)+12(x-5))=0$

$2(x-5)(x+12)=0$

Set Factors to equal 0:
$x-5=0$

$x=5$

or

$x+12=0$

$x=-12$

However, since we are solving for the side length, the only possible answer is 5 (a shape can't have a side with a negative length.)

The Solution Is:
$\boxed{x=5}$

I hope this helped!
-Benjamin

6 0

3 years ago

Plz solve it

konstantin123 [22]

Answer:

Fgh= -5x^3-^2+45x+9

Gfh= (3-x)(5x+1)(x+3)

I don't think you can do anything with the second one.

Step-by-step explanation:

8 0

3 years ago

What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the num

sleet_krkn [62]

Answer:

The discriminant is −4, so the equation has no real solutions.

Step-by-step explanation:

In the equation 0 = x² - 4x + 5, a is 1, b is -4, and c is 5.

Plug in these values into b² - 4ac, and simplify:

b² - 4ac

(-4)² - 4(1)(5)

16 - 20

= -4

So, the discriminant is -4. This means that the equation has no real solutions, because the discriminant is a negative number.

The correct answer is that The discriminant is −4, so the equation has no real solutions.

6 0

3 years ago

I need help with finding x.

Pepsi [2]

Get a hint and tell me when you get a hint of where the x and I’ll tell you

4 0

3 years ago

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