# Based on the estimates log(2) = .03 and log(5) = .7, how do you use properties of logarithms to find approximate values for log(80)?

Apr 22, 2018

0.82

#### Explanation:

we need to know the log property

$\log a \cdot b = \log a + \log b$

$\log \left(80\right) = \log \left(8 \cdot 10\right) = \log \left(8 \cdot 5 \cdot 2\right) = \log \left(4 \cdot 2 \cdot 5 \cdot 2\right) = \log \left(2 \cdot 2 \cdot 2 \cdot 5 \cdot 2\right)$

$\log \left(2 \cdot 2 \cdot 2 \cdot 5 \cdot 2\right) = \log 2 + \log 2 + \log 2 + \log 5 + \log 2 = 4 \log 2 + \log 5$

$4 \cdot \left(0.03\right) + 0.7 = 0.12 + 0.7 = 0.82$