Do You Know Your Log Properties?

Using the Properties of Logarithms , we can rewrite $\log _{7}35+\log _{7}35-\log _{7}25$

as

$\log_{7}[7\times5]+\log_{7}[7\times5]-\log_{7}[5\times5]$

$\Rightarrow \log_{7}7+\log_{7}5+\log_{7}7+\log_{7}5-[\log_{7}5+\log_{7}5]$

$\Rightarrow \log_{7}7 + \log_{7}7$

$\Rightarrow \boxed{2}$

$\log_{7}35 + \log_{7}35 - \log_{7}25 = \log_{7}\dfrac{35 \times 35}{25} = \log_{7}7^2 = \boxed{2}$

^7log((35)^2/25) = ^7log49 = 2