Question

Write log1/4(1/64)=3 in exponential form

Answer 1

For logarithmic equations,
log
b
(
x
)
=
y
log
b
(
x
)
=
y
is equivalent to
b
y
=
x
b
y
=
x
such that
x
>
0
x
>
0
,
b
>
0
b
>
0
, and
b
≠
1
b
≠
1
. In this case,
b
=
1
4
b
=
1
4
,
x
=
1
64
x
=
1
64
, and
y
=
3
y
=
3
.
b
=
1
4
b
=
1
4
x
=
1
64
x
=
1
64
y
=
3
y
=
3
Substitute the values of
b
b
,
x
x
, and
y
y
into the equation
b
y
=
x
b
y
=
x
.
(
1
4
)
3
=
1
64