Question

Solve the equation log(base 2) x-1/2log(base 2)(x + 1) = 1

Answer 1

Use the quotient property of logarithms,
log
b
(
x
)
−
log
b
(
y
)
=
log
b
(
x
y
)
log
b
(
x
)
-
log
b
(
y
)
=
log
b
(
x
y
)
.
log
2
(
x
+
2
x
−
5
)
=
3
log
2
(
x
+
2
x
-
5
)
=
3
Rewrite
log
2
(
x
+
2
x
−
5
)
=
3
log
2
(
x
+
2
x
-
5
)
=
3
in exponential form using the definition of a logarithm. If
x
x
and
b
b
are positive real numbers and
b
b
≠
≠
1
1
, then
log
b
(
x
)
=
y
log
b
(
x
)
=
y
is equivalent to
b
y
=
x
b
y
=
x
.
2
3
=
x
+
2
x
−
5
2
3
=
x
+
2
x
-
5
Solve for
x
x
Tap for more steps...
x
=
6