Question

log properties

Answer 1

\[\log \sqrt[5]{25x ^{2}} =\frac{ 1 }{3 }\log5x\]

Answer 2

quotient rule\[\huge\rm log_b y - \log_b x = \log_b \frac{ x }{ y}\]
to condense you can change subtraction to division
product rule \[\huge\rm log_b x + \log_b y = \log_b( x \times y )\]
addition ----> multiplication

power rule \[\huge\rm log_b x^y = y \log_b x\]
CHANGE OF BASE FORMULA:
change of base formula
\[\huge\rm log_a b = \frac{ \log b }{ \log a }\]

Answer 3

\[\large\rm log=\log_{10}\]
first apply power rule