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Pedro is given that log50−−√=0.8495. Without using a calculator, how can Pedro find log2√?



A log50−−√=log25−−√×log2√=5×log2√, so dividing 0.8495 by 5 will give the value of log2√.


B log50−−√=log25−−√+log2√=5+log2√, so subtracting 5 from 0.8495 will give the value of log2√.


C log100−−−√=log50−−√+log2√, and log100−−−√=1, so subtracting 0.8495 from 1 will give the value of log2√.


D log100−−−√=log50−−√×log2√, and log100−−−√=1, so dividing 1 by 0.8495 will give the value of log2√.

Respuesta :

Answer:

log 2 = 0.301

Step-by-step explanation:

We have to find the value of log 2 while the value of log 5 is given to be 0.6989.

Now, starting with log 10, we get,

log 10 = log (5 × 2) = log 5 + log 2

{Using the property of logarithm that, log AB = log A + log B}

⇒ [tex]\log 10^{1} = \log 5 + \log 2[/tex]

⇒ log 10 = 0.6989 + log 2

{Since [tex]\log x^{a} = a \log x[/tex]}

Again, we know that, log 10 = 1

⇒ 1 = 0.6989 + log 2

⇒ log 2 = 0.301 (Answer)

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