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4 years ago

Which equation is true for x = 6? A) 2x + 5 = 25 B) 3x + 5 = 17 C) 5x − 18 = 7 D) 6x − 10 = 26

Mathematics

1 answer:

Anit [1.1K]4 years ago

4 0

D is the answer.
6×6-10=26

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If <img src="https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20x%20%3D%20log_%7Ba%7D%28bc%29" id="TexFormula1" title="\rm \: x = log_{a}(

timama [110]

Use the change-of-basis identity,

$\log_x(y) = \dfrac{\ln(y)}{\ln(x)}$

to write

$xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}$

Use the product-to-sum identity,

$\log_x(yz) = \log_x(y) + \log_x(z)$

to write

$xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}$

Redistribute the factors on the left side as

$xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}$

and simplify to

$xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)$

Now expand the right side:

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}$

Simplify and rewrite using the logarithm properties mentioned earlier.

$xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1$

$xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}$

$xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}$

$xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)$

$\implies \boxed{xyz = x + y + z + 2}$

(C)

6 0

2 years ago

The police use a speed gun to monitor one part of a highway. During one hour, 6 out of 25 cars were traveling above the speed li

Vlad [161]

4 0

3 years ago

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What is 240 fl oz equal to in cups

Wewaii [24]

What is 240 fl oz equal to in cups?

1 fl oz = 0.125 cups

Convert:-

240 × 0.125 = 30

<span>240 fl oz = 30 cups</span>

7 0

3 years ago

.Rahul and his wife work in Mohan's farm. The Government has declared that the farm workers should be paid Rs. 71 for a day's wo

Snowcat [4.5K]

Answer:

Rs. 5500

Step-by-step explanation:

The government has declared that farm workers should be paid Rs. 71 for a day's work

The landlord Mohan pays Rahul Rs. 60 and pays Rs. 55 to his wife

Rahul works for 55 days

= 60 × 55

= Rs. 3,300

His wife works for 40 days

= 55 ×40

= Rs. 2,200

Therefore the total amount of money earned together can be calculated as follows

= 3300 + 2200

= Rs. 5500

Hence they will earn Rs. 5500 together

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3 years ago

I need help solving this trig problem w/ identites.

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$\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\\\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad \qquad sec(\theta)=\cfrac{1}{cos(\theta)}
\\\\
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$\bf \cfrac{1}{sin(x)-1}+\cfrac{1}{sin(x)+1}\implies \cfrac{sin(x)+1~~+~~sin(x)-1}{[sin(x)-1][sin(x)+1]}
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3 0

3 years ago