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VARVARA [1.3K]
3 years ago
11

Solve the following logarithmic equations. ln(x^6) = 36

Mathematics
1 answer:
Hoochie [10]3 years ago
8 0

Answer:

The solution is x = e⁶

Step-by-step explanation:

Hi there!

First, let´s write the equation

ln(x⁶) = 36

Apply logarithm property: ln(xᵃ) = a ln(x)

6 ln(x) = 36

Divide both sides of the equation by 6

ln(x) = 6

Apply e to both sides

e^(ln(x)) = e⁶

x = e⁶

The solution is x = e⁶

Let´s prove why e^(ln(x)) = x

Let´s consider this function:

y = e^(ln(x))

Apply ln to both sides of the equation

ln(y) = ln(e^(ln(x)))

Apply logarithm property: ln(xᵃ) = a ln(x)

ln(y) = ln(x) · ln(e)         (ln(e) = 1)

ln(y) = ln(x)

Apply logarithm equality rule: if ln(a) = ln(b) then, a = b

y = x

Since y = e^(ln(x)), then x =e^(ln(x))

Have a nice day!

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statuscvo [17]

Answer:

64

Step-by-step explanation:

its just how it is

8 0
2 years ago
The length of a rectangle is 3 more than the width fine the length if the perimeter is 98 inches
german

Answer - Width 23

Length - 26



W = Width


L + 3 = Length



Perimeter = 2L = 2W


98 = 2(W + 3) + 2W


98 = 2W + 6 + 2W


98 = 4W + 6


92 = 4W


W = 92/4


W = 23


Width is 23 inches

Length is 3 more -- 23 + 3 = 26



We can double check our work:


26 + 26 + 23 + 23 = 98 Inches



Best of luck,

The Artemis Wolf

3 0
3 years ago
A farmer has a piece of land with an area of 4 square yards. If a cow can graze grass at a rate of 2 square feet per hour, how l
Lunna [17]

Answer:

2 hours

Step-by-step explanation:

4 square yards to feet: 4*3 = 12ft

3 cows grazing grass at 2 ft per hour: 2*2 = 6 square ft per hour

Time taken: 12ft/6ft per hour = 2 hours

8 0
1 year ago
How do you round 3,979 rounded to the nearest thousand?
OlgaM077 [116]
We are going to round the number '3'.
Look at the first number to the right of '3', which is '9'.
That number is greater than '5', so you round the '3' to '4', and add three zeros after '4'.

Answer is: 4,000
6 0
3 years ago
Each side of a cube is 2 inches long what’s the volume of the cube
Kaylis [27]

Answer:

Step-by-step explanation:

The volume of a cube is s*s*s or s^3 where s = the length of a side (2 in this case).

V = s^3

V = 2^3

V = 2*2*2

V = 8 cu in or 8 in^3

4 0
3 years ago
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