Question

Log5 =0,699 find log 0,5

Answer 1

-0.301

Explanation:

Correct Question :-

If log 2 = 0.301 , find log 0.5

Solution :-

We are here given that the value of log 5 is 0.699 . Here the base of log is 10 .

`\rm\implies log_(10)2= 0.301`

And we are supposed to find out the value of log 0.5 . We can write it as ,

`\rm\implies log_(10)(0.5) = log _(10)\bigg( (5)/(10)\bigg)`

Simplify ,

`\rm\implies log _(10)\bigg( (1)/(2)\bigg)`

This can be written as ,

`\rm\implies log_(10) ( 2^(-1))`

Use property of log ,

`\rm\implies -1 * log_(10)2`

Put the value of log 2 ,

`\rm\implies -1 * 0.301 =\boxed{\blue{-0.301}}`

Hence the value of log (0.5) is -0.301 .

*Note -

Here here there was no use of log 5 in the calculation .