Question

Given that \(\log_{4n} 40\sqrt{3} = \log_{3n} 45\), find \(n^3\).

Answer 1

you should get to \( (\frac{4}{3})^y = \frac{40 \sqrt{3}}{45}\) by letting \(y = log_{4n}.... = log_{3n} ......\)

to find y, fiddle around with \(\frac{40 \sqrt{3}}{45}\) in a calculator. for example \((\frac{40 \sqrt{3}}{45})^2 = \frac{64}{27}\)

may be a smarter way to solve for y but that gets it going nicely