# How to calculate log 0.9821*10^6 ?

Jun 18, 2018

Should you not specify the BASE of the logarithmic function...?

#### Explanation:

If it is ${\log}_{10} 0.9821 \times {10}^{6}$...this is approx. equal to $6$...we get a more or less exact value from the calculator...${\log}_{10} 0.9821 \times {10}^{6} \equiv 5.992$...

But if we use natural logarithms (and since the base is UNSPECIFIED I would be justified in assuming this, the most natural base) we got...

${\log}_{e} 0.9821 \times {10}^{6} \equiv 13.797$...

As always when we write ${\log}_{a} b = c$...I ask to what power I raise the base $a$ to get $b$...and here ${a}^{c} = b$. By way of example....

${\log}_{10} \left(0.1\right) = {\log}_{10} \left({10}^{- 1}\right) = - 1$

${\log}_{10} \left(100\right) = {\log}_{10} \left({10}^{2}\right) = 2$

${\log}_{10} \left(1000000\right) = {\log}_{10} \left({10}^{+ 6}\right) = 6$

With me...?