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Which logarithmic equation is equivalent to the exponential equation below?

aleksandr82 [10.1K]

Option B: $\ln 6=5 x$ is the correct answer.

Explanation:

The exponential equation is $e^{5 x}=6$

If $f(x)=g(x)$ , then $\ln (f(x))=\ln (g(x))$

Thus, the equation becomes

$\ln \left(e^{5 x}\right)=\ln (6)$

Applying log rule, $\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)$ and thus the equation becomes

$5 x \ln (e)=\ln (6)$

Since, we know that, $\ln (e)=1$ , using this we get,

$5 x=\ln (6)$

Hence, the logarithmic equation which is equivalent to the exponential equation $e^{5 x}=6$ is $\ln 6=5 x$

Thus, Option B is the correct answer.

7 0

3 years ago

How many permutations can be formed from the letters of the word tennessee ?

Over [174]

<span>3780 If you consider every letter in the word "tennessee" to be unique there is 9!, or 362880 different ways to arrange the letters. So let's use that as a starting point. Now there's 4 e's, which we really don't care how they're arranged. So divide by 4!, or 24. Giving us 362880/24 = 15120 different ways to arrange the letters. There's also 2 n's. So divide by 2!, giving us 15120/2 = 7560 different ways. Don't forget the s's either. So another division by 2!, giving 7560/2 = 3780 different ways. And there's no more duplicate letters, so the final figure is 3780 different ways to arrange the letters in the word "tennessee".</span>

8 0

3 years ago

What’s the calculation of the equation 5/8-1/4=

Kay [80]

Answer: 3/8

Explanation: To subtract unlike fractions such as 5/8 - 1/4, first find a common denominator. The common denominator of 8 and 4 will be the least common multiple of 8 and 4 which is 8.

Notice that our first fraction already has 8 in the denominator so it stays the same. To get 8 in the denominator of 1/4, we multiply the numerator and denominator by 2 to get 2/8.

Now we have 5/8 - 2/8.

To subtract like fractions, we simply subtract the numerators to get 3 and keep our denominator of 8 and we have 3/8.

Since 3/8 is in lowest terms, it's our final answer.

Therefore, 5/8 - 1/4 = 3/8.

4 0

3 years ago

Will mark brainiest for simplest and most coherent answer. What does it mean if an x (input) or y (output) value doesn't make se

Maksim231197 [3]

Answer:

I tried to answer but I still would like to know what doesn't make sense.

Considering the identity:

$\sec^2\theta-\tan^2\theta=1 \implies |\sec\theta|\geq1$

$\forall\;\theta\in\mathbb{R}-\{(2n+1)\frac{\pi}{2}, n\in\mathbb{Z} \}$

The identity is true whenever both sides are defined. It is not supposed to hold the values when we have division by zero, because it is undefined.

If the value doesn't make sense, it is probably not a function, or it is undefined by the given value of $x$ .

Let's go back to the definition of function again:

A function relates a set of inputs and a set of allowable outputs where each input is related to only one output. It basically defines the relation of ordered pairs.

Hope it helped you a bit.

8 0

3 years ago

2 planes leave the airport at the same time. their speeds are 140 mph and 170 mph and the angle between their courses is 25 degr

Damm [24]

Answer:

183.27miles

Step-by-step explanation:

Note that we are considering two planes.

Plane 1

Speed = 140 mph

Time = 2.5 hours

Distance = ?

Speed = distance/time

140 mph = distance/2.5hrs

Distance = 140×2.5

= 350miles

Plane 2

Speed = 170 mph

Time = 2.5 hours

Distance = ?

Speed = distance/time

170 mph = distance/2.5hrs

Distance = 170×2.5

= 425miles

The angle between side is 25 degree

From cosine rule

c^2 = a^2 + b^2 − 2abcos(tetha)

Where a = 350

b = 425miles

c^2 = 350^2+425^2-2(350×425)(cos25)

c^2 = 122500+180625-297500(0.906)

c^2 = 303125-269535

c^2 = 33590

C = √33590

C = 183.27miles

The distance they flew apart after 2.5hrs is 183.27miles

5 0

3 years ago