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3 years ago

What is the first step in solving ln(x − 1) = ln6 − lnx for x?

Mathematics

2 answers:

Zarrin [17]3 years ago

8 0

The first step to solving this problem is Multiplying In(x-1).

JulsSmile [24]3 years ago

6 0

Answer:

The first step is to apply the laws of logarithms and write (In 6 - In x) as a single logarithms.

Solving he equation, x = 3 or x = -2.

Step-by-step explanation:

In (x - 1) = In 6 - In x

To solve this, we first apply the laws of logarithms and write (In 6 - In x) as a single logarithms.

In 6 - In x = In (6 ÷ x) = In (6/x)

In |(x - 1)| = In |(6/x)|

We can then say that

(x - 1) = (6/x)

x(x - 1) = 6

x² - x - 6 = 0

x² - 3x + 2x - 6 = 0

x(x - 3) + 2(x- 3) = 0

(x - 3)(x + 2) = 0

x = 3 or x = -2

Hope this Helps!!!

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Simple geometry please help<br><br> Find KL. Round to the nearest hundredth.

vivado [14]

Answer:

KL ≈ 1.94

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos48° = $\frac{adjacent}{hypotenuse}$ = $\frac{JL}{KL}$ = $\frac{1.3}{KL}$ ( multiply both sides by KL )

KL × cos48° = 1.3 ( divide both sides by cos48° )

KL = $\frac{1.3}{cos48}$ ≈ 1.94 ( to the nearest hundredth )

6 0

3 years ago

Find the value of x. Then find the measure of each labeled angle. x = 37.5; the labeled angles are 77.5º and 102.5º. x = 37.5; t

Ne4ueva [31]

Answer:

x = 25; both labeled angles are 65º

Step-by-step explanation:

To find the value of x, recall that the angles formed by two parallel lines on the same line are equal if they correspond to each other.

In the figure given above, we have two parallel line given. The angle formed by each parallel line is corresponding to the other. Therefore, both angles formed are equal.

Thus,

(3x - 10)° = (x + 40)°

Solve for x

3x - 10 = x + 40

Subtract x from both sides

3x - 10 - x = x + 40 - x

3x - x - 10 = x - x + 40

2x - 10 = 40

Add 10 to both sides

2x - 10 + 10 = 40 + 10

2x = 50

Divide both sides by 2

2x/2 = 50/2

x = 25

*Plug in the value of x to find the measure of each labelled angles:

(3x - 10)° = 3(25) - 10 = 75 - 10 = 65°

(x + 40)° = 25 + 40 = 65°

3 0

3 years ago

The speed of light is about 3x10^8 m/s what is the speed of light in kilometers per hour

BigorU [14]

$3*10^8 \frac{m}{s} \\\\ 1m\to 10^{-3}km \\\\ 1s\to 36*10^{-4} h \\\\\\ 3*10^8* \frac{10^{-3}km}{36*10^{-4}s}= 10^8 * \frac{10^{-3}*10^4km}{12s}= \\\\ =10^8* \frac{10m}{12s}= \\\\ =10^8* 83*10^{-2} \frac{m}{s}=\\\\= \boxed{83*10^6 \frac{m}{s}}$