Question

Express as a single natural logarithm

In 2 + In 8 - In 4
In 4
In 6
In 64

Answer 1

`\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( (x)/(y)\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \underline{\ln(2)+\ln(8)}-\ln(4)\implies \underline{\ln(2\cdot 8)}-\ln(4)\implies \ln(16)-\ln(4) \\\\\\ \ln\left(\cfrac{16}{4} \right)\implies \ln(4)`