If log_{10}^{2}=0.3010 and~log_{10}^{3}=0.4771 then find log10036

Question

If log_{10}^{2}=0.3010 and~log_{10}^{3}=0.4771 then find log10036

Answer 1

To find log10036, we can express 10036 as a product of numbers that we already have logarithms for.

10036 = 10000 * 1.0036

Now, we can use the properties of logarithms to break this down further:

log10000 = log(10^4) = 4*log10 = 4*1 = 4

log1.0036 = log(1.0036) = log(10^0.0036) = 0.0036*log10 ≈ 0.0036 * 1 = 0.0036

Therefore,

log10036 = log(10000 * 1.0036) = log10000 + log1.0036 = 4 + 0.0036 = 4.0036

So, log10036 = 4.0036.