can you help me to find N please ?

\(51.725 = {(1.005)^N - 1 \over 0.005(1.005)^N}\)

 

\(\begin{align} 51.725& = {(1.005)^N - 1 \over 0.005(1.005)^N}\\ 51.725* 0.005(1.005)^N& = (1.005)^N - 1 \\ 0.258625(1.005)^N - (1.005)^N &=- 1 \\ (0.258625-1)(1.005)^N& =- 1 \\ -0.741375(1.005)^N&=- 1 \\ (1.005)^N&=- 1\div -0.741375 \\ (1.005)^N&=1.348845051\\ log(1.005)^N&=log1.348845051\\ log(1.005)^N&=log1.348845051\\ Nlog(1.005)&=log1.348845051\\ N&=\frac{log(1.348845051)}{ log(1.005) } \\ N&\approx59.999 \end{align}\)

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