Given that $\ln 2=a$ and $\ln 5=b$. Express $\ln \sqrt[4]{50{{e}^{3}}}$ in terms of $a$ and

Question

Given that $\ln 2=a$ and $\ln 5=b$. Express $\ln \sqrt[4]{50{{e}^{3}}}$ in terms of $a$ and $b$. Find the value of $k$ such that $\ln k=\frac{b-3a}{2}$, give your answer to $4$ significant figures.

Accepted Answer

(a) $\frac{a+2b+3}{4}$. (b) $k=\sqrt{\frac58}=0.7906$ (4 s.f.).

Exponential and Logarithmic Functions - Laws of Logarithms

Exponential and Logarithmic Functions - Laws of Logarithms

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