Simplifying Logarithms: log a 2x + 3(log a x - log a y)
- Thread starter Moonseed
- Start date
pka
Elite Member
- Joined
- Jan 29, 2005
- Messages
- 11,984
\(\displaystyle \
\log _a (2x) + 3\left( {\log _a (x) - \log _a (y)} \right) = \log _a (2x) + 3\left( {\log _a \left( {\frac{x}{y}} \right)} \right) = \log _a (2x) + \left( {\log _a \left( {\frac{{x^3 }}{{y^3 }}} \right)} \right) = \left( {\log _a \left( {\frac{{2x^4 }}{{y^3 }}} \right)} \right)\)
\log _a (2x) + 3\left( {\log _a (x) - \log _a (y)} \right) = \log _a (2x) + 3\left( {\log _a \left( {\frac{x}{y}} \right)} \right) = \log _a (2x) + \left( {\log _a \left( {\frac{{x^3 }}{{y^3 }}} \right)} \right) = \left( {\log _a \left( {\frac{{2x^4 }}{{y^3 }}} \right)} \right)\)