If \displaystyle \frac{1}{3}\log _{3}M+3\log _{3}N=1+\log_{0. | Filo

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Class 11 Maths Algebra Logarithm and Antilogarithm

If

\frac{1}{3} lo g_{3} M + 3 lo g_{3} N = 1 + lo g_{0.008} 5

then

(a)

M^{9} = \frac{9}{N}

(b)

N^{9} = \frac{9}{M}

(c)

M^{3} = \frac{3}{N}

(d)

N^{9} = \frac{3}{M}

Correct answer: (b)

Solution:

\frac{1}{3} lo g_{3} M + 3 lo g_{3} N = 1 + lo g_{0.008} 5

\frac{1}{3} lo g_{3} M + 3 lo g_{3} N = 1 + \frac{lo g 5}{lo g 0 . 0 0 8}

\frac{1}{3} lo g_{3} M + 3 lo g_{3} N = 1 + \frac{lo g 5}{lo g \frac{8}{1 0 0 0}}

\frac{1}{3} lo g_{3} M + 3 lo g_{3} N = 1 + \frac{lo g 5}{lo g 8 - lo g 1 0 0 0}

\frac{1}{3} lo g_{3} M + 3 lo g_{3} N = 1 + \frac{lo g 5}{3 ( lo g 2 - lo g 1 0 )}

\frac{1}{3} lo g_{3} M + 3 lo g_{3} N = 1 + \frac{lo g 5}{3 ( lo g \frac{1}{5}}

lo g_{3} M^{\frac{1}{3}} N^{3} = 1 - \frac{1}{3}

lo g M^{\frac{1}{3}} N^{3} = \frac{2}{3} lo g 3

M^{\frac{1}{3}} N^{3} = 3^{\frac{2}{3}}

M N^{9} = 9

N^{9} = \frac{9}{M}

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Similar topics

determinants

matrices

binomial theorem

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determinants

matrices

binomial theorem

permutations and combinations

complex numbers and quadratic equations

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Express each of the following in a form free from logarithm :

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can be expressed as

F = G \frac{m _{1} m _{2}}{d ^{2}}

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If true write 1 and if false then write 0

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3^{x} = \frac{1}{9}

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Rewrite the following equalities in the exponential form.

l o g_{100} 0.1 = - \frac{1}{2}

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\frac{lo g x}{lo g y} = \frac{3}{2}

lo g (x y) = 5

, then number of zeros in

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Number of real values of

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x + lo g_{10} (1 + 2^{x}) = x lo g_{10} 5 + lo g_{10} 6

play button image

If mantissa of logarithm of 719.3 to the base 10 is 0.8569 , then mantissa of logarithm of 71.93 is

play button image

lo g_{10} 0.001

play button image

4^{3 / 2} = 8

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

3^{x} = \frac{1}{9}

x = ?

play button image

Rewrite the following equalities in the exponential form.

l o g_{100} 0.1 = - \frac{1}{2}

play button image

\frac{lo g x}{lo g y} = \frac{3}{2}

lo g (x y) = 5

, then number of zeros in

x \times y

play button image

Number of real values of

x

x + lo g_{10} (1 + 2^{x}) = x lo g_{10} 5 + lo g_{10} 6

play button image

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Privacy Policy and Terms & Conditions
Download App

Copyright FILO EDTECH PVT. LTD. 2021