Question

how to find log of 0.0136

Answer 1

-1.86646109163

HOW TO FIND:

Determine the mantissa of the number as if it were between 1 and 10, using your L scale. Then subtract the characteristic for the number of places the decimal point of your actual number is to the left of the whole single digit number.

Answer 2

{we know that,  

loga(pqr)=loga(p)+loga(q)+loga(r), loga(pn)=n∗loga(p) and, logn(b)=logn(b)logn(a)}

Now coming to problem: we have to find the value of 0.0136= 1.36*10-2

log10[1.36∗10^(-2)]=log10(136∗10^−2)+log10(10^−2)

log10(1.36∗10^−2)=log10(136)+log10(10^−2)+(−2)

log10(1.36∗10^−2)=log10(136)−2−2

log10(1.36∗10^−2)=log10(136)−4

log10(1.36∗10^−2)=[log3(136)/log310]−4

To find out logarithm of 136 to the base 3, let’s study 136.

As 136 < (3^5 or 243) and  

  136 > ( 3^4 or 81).

Also the number is less than the mean of 243 and 81 (i.e., 162). so clearly its logarithmic value is less than 4.5.

Let us assume its value to be 4.4. And the logarithmic value of 10 is 2 (as 10 is near to 3^2=9).

log10(1.36∗10^−2)=2.2−4

So the value of the above expression reduces to

log10(1.36∗10^−2)=−1.8

Answer: -1.8 approximately.