Please help! 10 points!

16^x = 64^x +4

1) X =-12

2) x=-2

3) X =2

4) x=12

Step-by-step explanation:

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Algebra Examples

Popular Problems Algebra Solve for x 64^(4x)=16^(x+1)

64

4

x

=

16

x

+

1

Create equivalent expressions in the equation that all have equal bases.

4

3

(

4

x

)

=

4

2

(

x

+

1

)

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

3

(

4

x

)

=

2

(

x

+

1

)

Solve for

x

.

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Multiply

4

by

3

.

12

x

=

2

(

x

+

1

)

Simplify

2

(

x

+

1

)

.

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Apply the distributive property.

12

x

=

2

x

+

2

⋅

1

Multiply

2

by

1

.

12

x

=

2

x

+

2

Move all terms containing

x

to the left side of the equation.

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Subtract

2

x

from both sides of the equation.

12

x

−

2

x

=

2

Subtract

2

x

from

12

x

.

10

x

=

2

Divide each term by

10

and simplify.

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Divide each term in

10

x

=

2

by

10

.

10

x

10

=

2

10

Cancel the common factor of

10

.

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Cancel the common factor.

10

x

10

=

2

10

Divide

x

by

1

.

x

=

2

10

Cancel the common factor of

2

and

10

.

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Factor

2

out of

2

.

x

=

2

(

1

)

10

Cancel the common factors.

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Factor

2

out of

10

.

x

=

2

⋅

1

2

⋅

5

Cancel the common factor.

x

=

2

⋅

1

2

⋅

5

Rewrite the expression.

x

=

1

5

The result can be shown in multiple forms.

Exact Form:

x

=

1

5

Decimal Form:

x

=

0.2

hard

step-by-step explanation: