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
topjm [15]
3 years ago
7

What is the equation of log x 729=3?

Mathematics
1 answer:
pishuonlain [190]3 years ago
7 0

Answer:

Step-by-step explanation:

Move 729  to the left side of the equation by subtracting it from both sides.  x  3 − 729  = 0  Factor the left side of the equation.  Rewrite  729  as 9

3

.  x

3

−

9

3

=

0

. Since both terms are perfect cubes, factor using the difference of cubes formula,  a

3

−

b

3

=

(

a

−

b

)

(

a

2+ab+b2). Where a

=x and  b=9. (x−9)(x2+x⋅9+92)=0

. Simplify.  Move 9  to the left of x

.  (x−9)(x2+9x+92)=0.  Raise  9  to the power of 2

.  (x

−9

)(

x

2

+

9

x

+81

)=0

. Set x

−9  equal to  0 and solve for x.  Set the factor equal to  0. x−

9=

0. Add 9  to both sides of the equation.  x=9

. Set x2+

9

x

+

81 equal to  0  and solve for  x

.  Set the factor equal to 0

.  x2+9x+81=0.  Use the quadratic formula to find the solutions.  −b±√b2−4(ac) 2a. Substitute the values  a=1, b=9, and c=81  into the quadratic formula and solve for  x.  −9±√92−4⋅ (1⋅81

) 2⋅

1  Simplify.  Simplify the numerator. Raise 9  to the power of 2. x=−9±√81−4⋅(1⋅81) 2⋅1. Multiply  

81

by  

1

.

x

=

−

9

±

√

81

−

4

⋅

81

2

⋅

1

Multiply  

−

4

by  

81

.

x

=

−

9

±

√

81

−

324

2

⋅

1

Subtract  

324

from  

81

.

x

=

−

9

±

√

−

243

2

⋅

1

Rewrite  

−

243

as  

−

1

(

243

)

.

x

=

−

9

±

√

−

1

⋅

243

2

⋅

1

Rewrite  

√

−

1

(

243

)

as  

√

−

1

⋅

√

243

.

x

=

−

9

±

√

−

1

⋅

√

243

2

⋅

1

Rewrite  

√

−

1

as  

i

.

x

=

−

9

±

i

⋅

√

243

2

⋅

1

Rewrite  

243

as  

9

2

⋅

3

.

Tap for fewer steps...

Factor  

81

out of  

243

.

x

=

−

9

±

i

⋅

√

81

(

3

)

2

⋅

1

Rewrite  

81

as  

9

2

.

x

=

−

9

±

i

⋅

√

9

2

⋅

3

2

⋅

1

Pull terms out from under the radical.

x

=

−

9

±

i

⋅

(

9

√

3

)

2

⋅

1

Move  

9

to the left of  

i

.

x

=

−

9

±

9

i

√

3

2

⋅

1

Multiply  

2

by  

1

.

x

=

−

9

±

9

i

√

3

2

Factor  

−

1

out of  

−

9

±

9

i

√

3

.

x

=

−

1

9

±

9

i

√

3

2

Multiply  

−

1

by  

−

1

.

x

=

1

−

9

±

9

i

√

3

2

Multiply  

−

9

±

9

i

√

3

by  

1

.

x

=

−

9

±

9

i

√

3

2

The final answer is the combination of both solutions.

x

=

−

9

−

9

i

√

3

2

,

−

9

+

9

i

√

3

2

The solution is the result of  

x

−

9

=

0

and  

x

2

+

9

x

+

81

=

0

.

x

=

9

,

−

9

−

9

i

√

3

2

,

−

9

+

i

√

3

2

You might be interested in
El precio de un ordenador portátil ha aumentado un 25% y posteriormente fue rebajado un cierto porcentaje.Calcule que porcentaje
ZanzabumX [31]

Answer:

Se requiere un 20 por ciento de descuento.

Step-by-step explanation:

(This exercise has been presented in Spanish and for that reason explanation will be held in the same language)

Sea p_{o} el precio original del computador portatil, el nuevo precio es:

p_{1} =\left(\frac{100\,\% + 25\,\%}{100\,\%} \right)\cdot p_{o}

p_{1} = 1.25\cdot p_{o}

Si p_{2} = p_{o}, entonces el porcentaje requerido para recuperar el precio original es:

r = \left(1-\frac{p_{2}}{p_{1}} \right)\times 100\,\%

r = \left(1-\frac{p_{o}}{1.25\cdot p_{o}} \right)\times 100\,\%

r = \left(1-\frac{1}{1.25} \right)\times 100\,\%

r = 20\,\%

Se requiere un 20 por ciento de descuento.

5 0
2 years ago
If you and a guy have been arguing lately and he’s friends with your ex best friend and she tried to get him to break up with yo
sashaice [31]

Answer: leave him

Step-by-step explanation:

5 0
3 years ago
If anyone could help it would be greatly appreciated
Ira Lisetskai [31]

Answer:

Step-by-step explanation:

area of one triangle=(1/2)×6×4=12 m²

area of four triangles=4×12=48 m²

area of square=6×6=36 m²

total area=48+36=84 m²

4 0
3 years ago
HELP PLEASE THANKS:(
astraxan [27]
2(2)+3y=13
4+3y=13
3y=9
y=3
The answer is B
6 0
3 years ago
If Sasha can run 720 yards in 4 minutes, how many feet can she run in 15 seconds?
Vika [28.1K]
Okay so you're trying to find the unit rate of 720yds/4min. If you divide 720 by 4 you will have the unit rate as 180yds/1 min or 60 sec then if you divide 180 and 60 by 4 again you will get the answer of 45yds/15sec.
6 0
3 years ago
Other questions:
  • The volume of the earth is 260,000,000,000 cubic miles? what is the volume in scientific notation
    12·1 answer
  • Please help me with questions 18 and 19
    12·1 answer
  • If the Williams family has a monthly income of $3,000, how much do they spend on food each month?
    8·2 answers
  • Since life expectancy has increased in the last century, the number of Alzheimer patients has increased dramatically. The number
    6·1 answer
  • f the polygon is translated 4 units down and 5 units right, what will the coordinates of the new image be
    10·1 answer
  • 2x + 1 ≤ 7 and -2x + 1 ≤ 9
    8·1 answer
  • (2.5), (0,3),(2,5)<br><br> Help I’ve been stuck at this for so long
    13·1 answer
  • A high school student named David Merrell did a study of how music affects the ability of rats to run a maze. He trained 71 rats
    9·1 answer
  • 7.
    15·2 answers
  • Please help me, I don’t know what to do
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!