Question

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

Answer 1

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}

⇒ $\log 10^{1} = \log 5 + \log 2$

⇒ log 10 = 0.6989 + log 2

{Since $\log x^{a} = a \log x$}

Again, we know that, log 10 = 1

⇒ 1 = 0.6989 + log 2

⇒ log 2 = 0.301 (Answer)