The value of x satisfying the following relation: | Logarithms Questions & Answers

Q:

The value of $(\frac{1}{\log_{3} 60} + \frac{1}{\log_{4} 60} + \frac{1}{\log_{5} 60}) i s$

A) 0	B) 1
C) 5	D) 60

Answer & Explanation Answer: B) 1

Explanation:

=> $\log_{60} (3 * 4 * 5)$

=> $\log_{60} (60)$

= 1

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Q:

$i f \log \frac{a}{b} + \log \frac{b}{a} = \log (a + b), t h e n$

A) a + b = 1	B) a - b = 1
C) a = b	D) ab=1

Answer & Explanation Answer: A) a + b = 1

Explanation:

$i f \log \frac{a}{b} + \log \frac{b}{a} = \log (a + b), t h e n$

$\log (a + b) = \log (\frac{a}{b} \times \frac{b}{a}) = \log 1$

so, a+b=1

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Q:

If log 27 = 1.431, then the value of log 9 is

A) 0.754	B) 0.854
C) 0.954	D) 0.654

Answer & Explanation Answer: C) 0.954

Explanation:

log 27 = 1.431
log $(3^{3})$ = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = log( $3^{2}$ )= 2 log 3 = (2 x 0.477) = 0.954

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Q:

Which of the following statements is not correct?

A) log10 = 1	B) log (2 + 3) = log (2 x 3)
C) log1 = 0	D) log (1 + 2 + 3) = log 1 + log 2 + log 3

Answer & Explanation Answer: B) log (2 + 3) = log (2 x 3)

Explanation:

log (2 + 3) = log 5

log (2 x 3) = log 2 + log 3

log (2 + 3) $\neq$ log (2 x 3)

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A) 1/3	B) -1/3
C) 3	D) None of these

The value of x satisfying the following relation:

$\log_{\frac{1}{2}} (x) = \log_{2} (3 x - 2)$