If log103 = 0.477 and log105 = 0.698, then what is the value of log50 4.50?
Answer
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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Shell
Noun: A hard rigid usually large covering of an animal.; The outside part of a fruit or seed.; Something like an external structure that resembles a shell.; A casing without substance.; The hard exterior of an egg.; A hard enclosing cover.
Verb: To take out of the shell.; To fall out of the shell.; To cast the external covering.; To gather shells from a beach.
"My mother collected shells at the beach."
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