What is the equation of log x 729=3?

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