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NSW Y12 Maths Standard 1 NSW Y12 Maths Standard 2 NSW Y12 Maths Advanced NSW Y12 Maths Extension 1 NSW Y12 Maths Extension 2

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NSW Y12 Maths - Advanced Series and Finance Logs with GPs

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Logs with GPs Theory

Logarithms may be used to solve more difficult applications of geometric series.\\ \textbf{Example}\\ Which term of 7,21, 63, is equal to 137781 ?\\ \textbf{Solution}\\ This is a GP where \(a=7\) and \(r=3\) \\ $\begin{aligned} \therefore \quad T_n & =a r^{n-1} \\ 137781 & =7 \times 3^{n-1} \\ 3^{n-1} & =19683 \\ \ln 3^{n-1} & =\ln 19683 \\ (n-1) \ln 3 & =\ln 19683 \\ n-1 & =\ln 19683 \div \ln 3 \\ n & =10 \end{aligned}$\\

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  • Logs with GPs - Video - Logarithms with GPs

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