Revise the laws of logarithms in order to solve logarithmic and exponential equations
Part ofMathsAlgebraic and trigonometric skills
Solve for \(x\textgreater0\), \(2{\log _a}x + {\log _a}2 = {\log _a}50\)
Remember one of the laws of logs: \(n{\log _a}x = {\log _a}{x^2}\)
Another one of the laws are used here: \({\log _a}x + {\log _a}y = {\log _a}xy\)
\(2{\log _a}x + {\log _a}2 = {\log _a}50\)
\({\log _a}{x^2} + {\log _a}2 = {\log _a}50\)
\({\log _a}2{x^2} = {\log _a}50\)
\(2{x^2} = 50\)
\({x^2} = \frac{{50}}{2}\)
\({x^2} = 25\)
\(x = \pm 5\)
\(x = 5\) since \(x\textgreater0\)
