Find x if log1218 = log24x + | Logarithms Questions & Answers

Q:

If $l o g_{\sqrt{8}} (x) = 3 \frac{1}{3} t h e n f i n d t h e v a l u e o f x ?$

A) 25	B) 32
C) 37	D) None of these

Answer & Explanation Answer: B) 32

Explanation:

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Q:

$T h e v a l u e o f l o g_{2} (l o g_{5} (625)) i s :$

A) 2	B) 5
C) 10	D) 15

Answer & Explanation Answer: A) 2

Explanation:

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Q:

The value of $l o g_{343} (7) i s :$

A) 1/3	B) -3
C) -1/3	D) 3

Answer & Explanation Answer: A) 1/3

Explanation:

$\log_{343} (7) \log_{7^{3}} (7) \frac{1}{3} \log_{7} (7) W e k n o w t h a t l o g_{x} (x) = 1 = > \frac{1}{3}$

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Q:

If log 2 = 0.3010 and log 3 = 0.4771, the values of log₅ 512 is

A) 2.875	B) 3.875
C) 4.875	D) 5.875

Answer & Explanation Answer: B) 3.875

Explanation:

ANS: log₅512 = log512/log5 = $\frac{\log 2^{9}}{\log (10 / 2)}$ = $\frac{9 \log 2}{\log 10 - \log 2}$ = $\frac{9 * 0.3010}{1 - 0.3010}$ =2.709/0.699 =2709/699 =3.876

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Q:

If log 2 = 0.30103, Find the number of digits in 2⁵⁶ is

A) 17	B) 19
C) 23	D) 25

Answer & Explanation Answer: A) 17

Explanation:

$\log (2^{56})$ =56*0.30103 =16.85768.

Its characteristics is 16.

Hence, the number of digits in $2^{56}$ is 17.

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Q:

What is the characteristic of the logarithm of 0.0000134?

A) 5	B) -5
C) 6	D) -6

Answer & Explanation Answer: B) -5

Explanation:

log (0.0000134). Since there are four zeros between the decimal point and
the first significant digit, the characteristic is –5.

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Q:

If $\log_{x} (\frac{9}{16}) = - \frac{1}{2}, t h e n t h e v a l u e o f x ?$

A) -3/4	B) 3/4
C) 81/256	D) 256/81

Answer & Explanation Answer: D) 256/81

Explanation:

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Q:

if $\log_{10} 5 + \log (5 x + 1) = \log_{10} (x + 5) + 1, t h e n x i s e q u a l t o$

A) 1	B) 3
C) 5	D) 10

Answer & Explanation Answer: B) 3

Explanation:

$\log_{10} 5 + \log (5 x + 1) = \log_{10} (x + 5) + 1$

$\log_{10} [5 (5 x + 1)] = \log_{10} [10 (x + 5)]$

$5 (5 x + 1) = 10 (x + 5)$

5x+1=2x+10

3x=9

x=3

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Find x if

$l o g_{\frac{1}{\sqrt{2}}} (\frac{1}{\sqrt{8}}) = l o g_{2} (4^{x} + 1) . l o g_{2} (4^{x + 1} + 4)$

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Find x if log1218 = log24x + 1. log24x+1 + 4

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Find x if

$l o g_{\frac{1}{\sqrt{2}}} (\frac{1}{\sqrt{8}}) = l o g_{2} (4^{x} + 1) . l o g_{2} (4^{x + 1} + 4)$