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
UVOISINOULLIV HU
Gala2k [10]
<h3>Total snow fall for three days is 8.75 inches</h3>

<em><u>Solution:</u></em>

Given that,

Snow fell over the past three days

First\ day = 3\frac{2}{4}\ inches = \frac{14}{4}\ inches\\\\Second\ day = 3\frac{2}{4}\ inches = \frac{14}{4}\ inches\\\\Third\ day = 1\frac{3}{4}\ inches = \frac{7}{4}\ inches

<em><u>What was the total snowfall for the three days?</u></em>

Total snowfall = first day + second day + third day

Total\ snowfall = \frac{14}{4} + \frac{14}{4} + \frac{7}{4}\\\\Total\ snowfall = \frac{14 + 14 + 7}{4}\\\\Total\ snowfall = \frac{35}{4} \text{ or } 8.75\ inches

Thus total snow fall for three days is 8.75 inches

5 0
3 years ago
How to solve 15=x-3 ;_;
Vitek1552 [10]
X= 18

So that you can help yourself better use Math-way!!
3 0
3 years ago
Read 2 more answers
Identify the interval​
Maru [420]

Answer:

Octave

Step-by-step explanation:

F to F is an Octave.

8 0
2 years ago
which is not a result of multiplying the height of a rectangular prism by a scale factor of 1/2 and I need work to
chubhunter [2.5K]
C is the answer


for example

assume that the height of a rectangular prism is 2, width is 1 and length measures 3

the volume will be 6
(2*1*3)

if we multiply height with the scale factor of 1/2
it becomes 1

so the volume will be 3
(1*1*3)

this situation goes for other examples, too


good luck
5 0
3 years ago
SOMEONE HELP BECAUSE I DONT GET THIS
Leno4ka [110]

Answer:

x = 18

m<A = 166°

Step-by-step explanation:

The parallel lines are cut by a transversal, so corresponding angles A and B are congruent.

7x + 40 = 3x + 112

4x = 72

x = 18

m<A = 7x + 40 = 7(18) + 40 = 126 + 40 = 166

6 0
2 years ago
Read 2 more answers
Other questions:
  • Please help ASAP
    10·1 answer
  • Beau has decided to use the method of elimination to solve the system of equations as shown below.
    5·1 answer
  • Jenny is a 60% free-throw shooter. She gets to shoot a second free throw if and only if she makes her first shot. She can score
    6·2 answers
  • What is the distance between the following points?
    8·1 answer
  • Write as a product 27a^3−(a−b)^3
    12·1 answer
  • PLZZZZZZ HELP!!!!! WILL MARK U AS BRAINIEST FOR BEST ANSWER!!!!! IT HAS TO BE AN LETTER !!!!!
    11·1 answer
  • Please help me ASAP i give brainliests and thanks :)
    15·2 answers
  • Hey can someone help me!! in need of help!! ASAPPPP
    14·1 answer
  • A college has a student to teacher ratio of 35 to 2. If there are 170 teachers at the college, how many students attend the
    9·1 answer
  • A company that makes hair-care products had 2,000 people try a new shampoo. Of the 2,000 people, 4 had a mild allergic reaction.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!