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svetoff [14.1K]
3 years ago
8

Please help me with logarithms!

Mathematics
2 answers:
Dmitry [639]3 years ago
3 0

Answer:

x=2ln(2)/(2ln(2)-ln(3))

Step-by-step explanation:

ln(4^x-1)=ln(3^x)

(x-1)ln(4)=ln(3^x)

(x-1)ln(4)=xln(3)

ln(4)x-ln(4)=xln(3)

ln(4)x=ln(3)x+2ln(2)

2ln(2)x-ln(3)x=2ln(2)

(2ln(2)-ln(3))x=2ln(2)

Therefore, x=2ln(2)/(2ln(2)-ln(3))

Liula [17]3 years ago
3 0

Answer:

4.819 =x

Step-by-step explanation:

4^(x-1) = 3^x

Take the log of each side

log (4^(x-1)) = log(3^x)

We know that log a^b = blog a

(x-1)  log 4 = x log (3)

Distribute

x log 4 -log 4 = x log 3

Subtract x log 4 from each side

x log 4 - x log 4 -log 4 = x log 3 - x log 4

- log 4 = x log 3 - x log 4

Factor out -x

- log 4 =- x ( log 4- log 3)

Divide by -1

log 4 = x (log 4 - log 3)

Divide each side by  (log 4 - log 3)

log 4 /  (log 4 - log 3) = x

4.81884167930641800 =x

Round to the nearest thousandth

4.819 =x

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How many qt equal to 5 gal
Naily [24]
20 quarts equal 5 gallons. There are 4 quarts in a gallon so:


4 x 5 = 20
7 0
3 years ago
A man starts at a point A and walks 18 feet north. He then turns and walks due east at 18 feet per second. If a searchlight plac
34kurt

Answer:

1/10 per sec

Step-by-step explanation:

When he's walked x feet in the eastward direction, the angle Θ that the search light makes has tangent

tanΘ = x/18

Taking the derivative with respect to time

sec²Θ dΘ/dt = 1/18 dx/dt.

He's walking at a rate of 18 ft/sec, so dx/dt = 18.

After 3seconds,

Speed = distance/time

18ft/sec =distance/3secs

x = 18 ft/sec (3 sec)

= 54ft. At this moment

tanΘ = 54/18

= 3

sec²Θ = 1 + tan²Θ

1 + 3² = 1+9

= 10

So at this moment

10 dΘ/dt = (1/18ft) 18 ft/sec = 1

10dΘ/dt = 1

dΘ/dt = 1/10 per sec

8 0
3 years ago
Which of these is a unit of density?<br> Please help.
katen-ka-za [31]

Answer:

I think is C.

Step-by-step explanation:

Hope it's help you ❤️❤️❤️❤️❤️❤️❤️

7 0
3 years ago
Read 2 more answers
can someone please explain to me how to answer this question and also the equation to find the answer
Leona [35]
If #peaches = x and #plums = y we can write the following equations:

x+y=15
0.89x + 0.39y = 8.85

and x and y are whole numbers.

converting the first to x=15-y and plugging it into the second, you get

0.89(15-y) + 0.39y = 8.85 =>
13.35 - 0.89y + 0.39y = 8.85 =>
4.5 = 0.5y =>
y = 9

so x = 15-9 = 6

She bought 9 plums and 6 peaches.


6 0
3 years ago
The weights of packs of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation 2.4
Verdich [7]

A Z-score helps us to understand how far is the data from the mean. The correct option is B.

<h3>What is Z-score?</h3>

A Z-score helps us to understand how far is the data from the mean. It is a measure of how many times the data is above or below the mean. It is given by the formula,

Z = \dfrac{X- \mu}{\sigma}

Where Z is the Z-score,

X is the data point,

μ is the mean and σ is the standard variable.

The weight of a randomly selected pack of gum has a z-score of 3.11. Therefore, The weight of this pack of gum is heavier than the mean weight by 3.11 standard deviations.

Hence, the correct option is B.

Learn more about Z-score:

brainly.com/question/13299273

#SPJ1

4 0
2 years ago
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