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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:

\frac{x}{y ^{2}} + \frac{y}{x ^{2}} = \frac{9}{8}

x^{3} + y^{3} = \frac{9}{8} (x y)^{2} \to 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 \to 2

From

1

and

2

x^{3} + (\frac{8}{x})^{3} = \frac{9}{8} (8)^{2}

x^{6} + (8)^{3} = (72) x^{3}

x^{6} - 72 x^{3} + (8)^{3} = 0

x^{3} = \frac{7 2 \pm ( 7 2 ) ^{2} - 4 ( 8 ) ^{3}}{2} = \frac{7 2 \pm ( 5 6 ) ^{2}}{2}

x^{3} = \frac{7 2 \pm 5 6}{2} = 64, 8

x = 2, 4

From

2

:

x y = 8

y = \frac{8}{x} y = \frac{8}{2} = 4, y = \frac{8}{4} = 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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determinants

matrices

binomial theorem

permutations and combinations

complex numbers and quadratic equations

l o g_{2}

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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 \frac{m _{1} m _{2}}{d ^{2}}

.
If true write 1 and if false then write 0

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Write the following in exponential form:

lo g_{10} 100 = 2

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l o g_{10} 2 + 16 l o g_{10} \frac{1 6}{1 5} + 12 l o g_{10} \frac{2 5}{2 4} + 7 l o g_{10} \frac{8 1}{8 0}

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Rewrite the following equations in the logarithm from :

(22)^{- 2 / 3} = \frac{1}{2} .

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If the equation

2^{x} + 4^{y} = 2^{y} + 4^{x}

y

x

x < 0

, then the sum of the solutions will be

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Write the following in the power form :

lo g_{2} 4 = 4

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Solve the following equation:

lo g^{2} (100 x) + lo g^{2} (10 x) = 14 + lo g \frac{1}{x}

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l o g_{2}

play button image

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 \frac{m _{1} m _{2}}{d ^{2}}

.
If true write 1 and if false then write 0

play button image

Write the following in exponential form:

lo g_{10} 100 = 2

play button image

l o g_{10} 2 + 16 l o g_{10} \frac{1 6}{1 5} + 12 l o g_{10} \frac{2 5}{2 4} + 7 l o g_{10} \frac{8 1}{8 0}

play button image

Rewrite the following equations in the logarithm from :

(22)^{- 2 / 3} = \frac{1}{2} .

play button image

If the equation

2^{x} + 4^{y} = 2^{y} + 4^{x}

y

x

x < 0

, then the sum of the solutions will be

play button image

Write the following in the power form :

lo g_{2} 4 = 4

play button image

Solve the following equation:

lo g^{2} (100 x) + lo g^{2} (10 x) = 14 + lo g \frac{1}{x}

play button image

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Privacy Policy and Terms & Conditions
Download App

Copyright FILO EDTECH PVT. LTD. 2021