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Class 11
Maths
Algebra
Logarithm and Antilogarithm
Solve the following system of equations.
\displaystyle\, \frac{x}{y^2} + \frac{y}{x^2} = \frac{9}{8}, \log_2\, x + \log_\sqrt{2}\, \sqrt{y} = 3
Solution:
y
2
x
+
x
2
y
=
8
9
x
3
+
y
3
=
8
9
(
x
y
)
2
→
1
lo
g
2
x
+
lo
g
2
y
=
3
lo
g
2
x
+
lo
g
2
y
=
3
lo
g
2
x
=
3
(
x
y
)
=
2
3
=
8
(
x
y
)
=
8
→
2
From
1
and
2
x
3
+
(
x
8
)
3
=
8
9
(
8
)
2
x
6
+
(
8
)
3
=
(
7
2
)
x
3
x
6
−
7
2
x
3
+
(
8
)
3
=
0
x
3
=
2
7
2
±
(
7
2
)
2
−
4
(
8
)
3
=
2
7
2
±
(
5
6
)
2
x
3
=
2
7
2
±
5
6
=
6
4
,
8
x
=
2
,
4
From
2
:
x
y
=
8
y
=
x
8
y
=
2
8
=
4
,
y
=
4
8
=
2
(
x
,
y
)
:
(
2
,
4
)
,
(
4
,
2
)
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Similar topics
determinants
matrices
binomial theorem
permutations and combinations
complex numbers and quadratic equations
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View Similar topics ->
determinants
matrices
binomial theorem
permutations and combinations
complex numbers and quadratic equations
View All ↓
The value of
l
o
g
2
16 is
Express each of the following in a form free from logarithm :
lo
g
F
=
lo
g
G
+
lo
g
m
1
+
lo
g
m
2
−
2
lo
g
d
can be expressed as
F
=
G
d
2
m
1
m
2
.
If true write 1 and if false then write 0
Write the following in exponential form:
lo
g
1
0
1
0
0
=
2
The value of
l
o
g
1
0
2
+
1
6
l
o
g
1
0
1
5
1
6
+
1
2
l
o
g
1
0
2
4
2
5
+
7
l
o
g
1
0
8
0
8
1
is
Rewrite the following equations in the logarithm from :
(
2
2
)
−
2
/
3
=
2
1
.
If the equation
2
x
+
4
y
=
2
y
+
4
x
is solved for
y
in terms of
x
, where
x
<
0
, then the sum of the solutions will be
Write the following in the power form :
lo
g
2
4
=
4
Solve the following equation:
lo
g
2
(
1
0
0
x
)
+
lo
g
2
(
1
0
x
)
=
1
4
+
lo
g
x
1
The value of
l
o
g
2
16 is
Express each of the following in a form free from logarithm :
lo
g
F
=
lo
g
G
+
lo
g
m
1
+
lo
g
m
2
−
2
lo
g
d
can be expressed as
F
=
G
d
2
m
1
m
2
.
If true write 1 and if false then write 0
Write the following in exponential form:
lo
g
1
0
1
0
0
=
2
The value of
l
o
g
1
0
2
+
1
6
l
o
g
1
0
1
5
1
6
+
1
2
l
o
g
1
0
2
4
2
5
+
7
l
o
g
1
0
8
0
8
1
is
Rewrite the following equations in the logarithm from :
(
2
2
)
−
2
/
3
=
2
1
.
If the equation
2
x
+
4
y
=
2
y
+
4
x
is solved for
y
in terms of
x
, where
x
<
0
, then the sum of the solutions will be
Write the following in the power form :
lo
g
2
4
=
4
Solve the following equation:
lo
g
2
(
1
0
0
x
)
+
lo
g
2
(
1
0
x
)
=
1
4
+
lo
g
x
1
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