Question of The Day11-01-2021

If log103 = 0.477 and log105 = 0.698, then what is the value of log50 4.50?

Correct Answer : d ) 0.384

Explanation :

We know that,

$$log_b\ a= {log_c\ a\over log_c\ b}=log_c\ a-log_c\ b,$$ and $$log_c\ ab=log_c\ a+log_c\ b$$

Now, considering the given expression

log504.50

$$log_{10}\ 4.5\over log_{10}\ 50$$

$${log_{10}\ {45\over10}\over log_{10}\ 50}={log_{10}\ {(5×9)}-log_{10}\ 10 \over log_{10}\ {(5×10)}}$$

⇒l$$log_{10}\ 5+log_{10}\ 3^2-log_{10}\ 10\over log_{10}\ 5+log_{10}\ 10$$

We know that,

$$log\ a^m=m\ log \ a$$ and $$log_{10} \ 10 = 1$$

$$log_{10}\ 5+2log_{10}\ 3-log_{10}\ 10 \over log_{10}\ 5+log_{10}\ 10$$

From the given values,

$${{0.698+2×0.477-1}\over {0.698+1}}={0.652\over1.698}≈0.3839$$

Hence, (d) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA etc.

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