log, start base, 4, end base, start fraction, 1, divided by, 2, end fraction

log

4

(

1

64

)

Rewrite as an equation.

log

4

(

1

64

)

=

x

Rewrite

log

4

(

1

64

)

=

x

in exponential form using the definition of a logarithm. If

x

and

b

are positive real numbers and

b

does not equal

1

, then

log

b

(

x

)

=

y

is equivalent to

b

y

=

x

.

4

x

=

1

64

Create expressions in the equation that all have equal bases.

(

2

2

)

x

=

2

−

6

Rewrite

(

2

2

)

x

as

2

2

x

.

2

2

x

=

2

−

6

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

2

x

=

−

6

Solve for

x

.

x

=

−

3

The variable

x

is equal to

−

3

.

−

3

Step-by-step explanation: