How do you use properties of Logarithms to rewrite the following as the logarithm of a single number (no decimal values) 2 log 7 + log 3?

Jul 6, 2015

$2 \log 7 + \log 3 = \log 147$

Explanation:

First Property: $\log \left({x}^{d}\right) = \mathrm{dl} o g x$ or $\mathrm{dl} o g x = \log \left({x}^{d}\right)$

So

$2 \log 7 + \log 3 = \log \left({7}^{2}\right) + \log 3$

$2 \log 7 + \log 3 = \log 49 + \log 3$

Second Property: $\log \left(x y\right) = \log x + \log y$ or $\log x + \log y = \log \left(x y\right)$

So

2log 7+ log3 = log 49 + log 3 = log(49×3)

$2 \log 7 + \log 3 = \log 147$