# How do you evaluate log 1500?

Sep 9, 2015

$2 \log 2 + \log 3 + 3 \log 5$

#### Explanation:

Well we have

$\log 1500 = \log \left(15 \cdot 100\right) = \log 15 + \log 100$

$= \log \left(3 \cdot 5\right) + \log {10}^{2}$

$= \log 3 + \log 5 + 2 \log 10$

$= 2 \log 10 + \log 3 + \log 5$

$= 2 \log \left(2 \cdot 5\right) + \log 3 + \log 5$

$= 2 \log 2 + \log 3 + 3 \log 5$

Sep 10, 2015

If $\log$ here is common log (base 10), then $\log 1500 = 2 + \log 15$

#### Explanation:

If $\log 1500$ means ${\log}_{10} 1500$, then we have:

$\log 1500 = \log \left(100 \cdot 15\right)$

$= \log 100 + \log 15$

$= \log {10}^{2} + \log 15$

$= 2 + \log 15$

If you are using tables of logarithms, you'll need scientific notation:

$\log 1500 = \log \left(1.5 \cdot {10}^{3}\right)$

$= 3 + \log \left(1.5\right)$

$= 3 + 0.1761$ (from table)

$= 3.1761$