Question

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

Answer 1

`\log \:_(10)\left((1)/(2)\right)=-\log \:_(10)\left(2\right)=-0.30102`

Thus, option A is true.

Explanation:

Given the expression

`log\left((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((1)/(2)\right)=-\log \:_(10)\left(2\right)=-0.30103`

Therefore, option A is true.