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zvonat [6]
2 years ago
14

Without using logarithm tables, find the value of x given that: 2log2/3 = 1/2logx - log 18 + log 16

Mathematics
1 answer:
sweet-ann [11.9K]2 years ago
5 0

Answer:

x=\frac{1}{4}

Step-by-step explanation:

<u>Given:</u>

2log(\frac{2}{3})=\frac{1}{2}log(x)-log(18)+log(16)

<u>Use the Power Rule Law:</u>

log(\frac{2}{3}^2)=log(x^{1/2})+log(16)-log(18)

<u>Use the Quotient Rule Law:</u>

log(\frac{4}{9})=log(\sqrt{x})+log(\frac{16}{18})

<u>Use the Product Rule Law:</u>

log(\frac{4}{9})=log(\frac{16\sqrt{x}}{18})

<u>Simplify:</u>

log(\frac{4}{9})=log(\frac{8\sqrt{x}}{9})

\frac{4}{9}=\frac{8\sqrt{x}}{9}

4=8\sqrt{x}

\frac{4}{8}=\sqrt{x}

\frac{1}{2}=\sqrt{x}

\frac{1}{4}=x

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15 points please help!! :)<br> Find the value of x.
andriy [413]

Answer:

Question 4: -11

Question 5: -7

Step-by-step explanation:

Four

Every triangle has 180 degrees.

So all three angles add to 180

<em><u>Equation</u></em>

60 + 80 + x + 51 = 180

<em><u>Solution</u></em>

Combine the like terms on the left. This is the first time I've seen x be a negative value. Almost all of the time it isn't, which should make you wonder.

191 + x = 180    

Subtract 191 from both sides.

191 - 191 + x = 180 - 191

x = - 11

Five

If a triangle is a right triangle and one of the angles is 45, then so is the other one.

<em><u>Proof</u></em>

a + 45 + 90 = 180         Combine like terms on the left

a + 135 = 180                Subtract 135 on both sides.

a + 135-135=180-135    Combine the like terms

a = 45

<em><u>Statement</u></em>

That means 52 + x = 45 and here is another negative answer. Subtract 52 from both sides

52 - 52 + x = 45 - 52    Combine like terms.

x  = - 7

6 0
3 years ago
Read 2 more answers
A farmer ships oranges in wooden crates. Suppose each orange weighs the same amount. The total weight of a crate filled with ora
maw [93]

Answer: g= 25 oranges

Step-by-step explanation:

.38g + 15 = 24.5

.38g = 24.5 - 15

.38g = 9.5

g = 9.5 ÷ .38

g = 25

7 0
3 years ago
It is 4 1/2 miles to the end of the trail. If Sophia bikes to the end and back in 60 minutes, what is her average speed in miles
PtichkaEL [24]
60 minutes for 2 times of 4.5 miles

60 minutes for 9 miles.

9 miles/60 minutes = 9 miles/1 hour

9 mph
4 0
3 years ago
Lest year Joe scored 80 point on his moth exam
mixer [17]

Answer:

20%

Step-by-step explanation:

decreased score= 80-64 = 16

x% of 80 = 16

x=20

5 0
3 years ago
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A right triangle has legs measuring 4.5 meters and 1.5 meters. The length of tge legs of a second triangle are proportional to t
Leviafan [203]
If the legs of both triangles are supposed to be proportional then they would be equal in length because that's what proportional means

so if the legs of one triangle are 4.5 and 1.5 then the other triangle "if proportional" would have legs with the same measurements which are 4.5 and 1.5

hope this answers your question
8 0
3 years ago
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