Question

a) -0.30103 b) -1.69897 c) 9.69897 d) 0.69897​

Answer 1

Answer:

$\log \:_{10}\left(\frac{1}{2}\right)=-\log \:_{10}\left(2\right)=-0.30102$

Thus, option A is true.

Step-by-step explanation:

Given the expression

$log\left(\frac{1}{2}\right)$

$=\log _{10}\left(2^{-1}\right)$

$\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right),\:\quad \:x>0$

$\log _{10}\left(2^{-1}\right)=-1\cdot \log _{10}\left(2\right)$

so the expression becomes

$=-1\cdot \log _{10}\left(2\right)$

$\mathrm{Multiply:}\:1\cdot \log _{10}\left(2\right)=\log _{10}\left(2\right)$

$=-\log _{10}\left(2\right)$

substituting the value of log 2 = 0.30103

$\:=-0.30102$

Thus,

$\log \:_{10}\left(\frac{1}{2}\right)=-\log \:_{10}\left(2\right)=-0.30103$

Therefore, option A is true.