# Given log4=0.6021, log9=0.9542, and log12=1.-792, how do you find log 4.096?

Jan 13, 2017

$\log 4.096 = 0.6126$

#### Explanation:

$\log 4.096$

= $\log \frac{4096}{1000}$

= $\log 4096 - \log 1000$

and as factors of $4096 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = {2}^{12} = {4}^{6}$

= $\log {4}^{6} - 3$

= $6 \log 2 - 3$

= $6 \times 0.6021 - 3$

= $3.6126 - 3$

= $0.6126$

Note: We do not need $\log 9 = 0.9542$, and $\log 12 = 1.0792$. Further, if you check you will find $\log 4.096 = 0.6124$. The difference is due to rounding off.