1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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!

You might be interested in
Through (4,-4) ; perpendicular to 6y=x-12
BARSIC [14]

y = mx + b

m = slope and b = y-intercept


We can arrange 6y = x - 12 in the form of y = mx + b

                  6y = x - 12

                    y = 1/6(x) - 2

Slope of y = 1/6(x) - 2 is 1/6. Taking the negative reciprocal of the slope we get the slope for the perpendicular line.

Negative reciprocal of 1/6 is -6.

The equation for the perpendicular line is

                  y = -6x + b

To find b we can plug in the x and y values of (4,-4) into it since it passes through those coordinates

                -4 = -6(4) + b

                 b = -4 + 6(4)

                 b = -4 + 24

                 b = 20

So the equation for the perpendicular line is y = -6x + 20

3 0
3 years ago
Is this correct if not can someone give me the answer I will mark u brilliant
Mila [183]

Answer: the first one is 735.75

the second one is 69

Step-by-step explanation:

THEY ARE BOTH CORRECT!

4 0
3 years ago
Read 2 more answers
Which is larger than 8.15: 55/9 or 57/7 or 41/5 or 65/8​
grin007 [14]
55/9 = 6.11
57/7 = 8.14
41/5 = 8.2
65/8 = 8.125

The answer is 41/5 is larger than 8.15
3 0
2 years ago
Read 2 more answers
1 Anthony purchased a car for $9,400. He paid 6.5% sales tax. How much tax did he pay?​
KiRa [710]

Answer:

$8789

Step-by-step explanation:

you suptract 9,400. and 6.5%

5 0
3 years ago
Read 2 more answers
Pls somebody help me with this question​
Olin [163]
The answer would be B
6 0
3 years ago
Other questions:
  • Ethan writes 1/6 of a page in 1/12 of a minute. How much time does it take him to write a full page?
    9·2 answers
  • Identify the equation of the parent function, y=x3, that is horizontally stretched by a factor of 1/5 and reflected over the y-a
    12·2 answers
  • Are 3+4x and 4x+3 equivalent
    10·1 answer
  • Complete the conditional statement if -2 a&gt;6 then<br> A. A&gt;3<br> B. A &lt;3<br> C. A &lt;-3
    10·1 answer
  • 1a. 182 Freshmen were surveyed on whether they participate in a sport. 110 said yes, 40 boys said no, 90 girls were in the surve
    10·1 answer
  • What is the meaning of cubed (enter the number only)
    5·2 answers
  • Please help it’s due in 30 mins and I still have a lot more questions :(
    8·1 answer
  • I NEEDDD HELPPPP PLEASE ILL GIVE U BRAINLEST
    8·2 answers
  • What is it 150x8-10+25=
    13·2 answers
  • Answer it and you get points
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!