Question

Calculati log2(3) * log3(4) * log4(5)*...* log7(8)

Answer 1

$\displaystyle \mathtt{log_23\cdot log_34\cdot log_45\cdot ...\cdot log_78= \frac{lg3}{lg2} \cdot \frac{lg4}{lg3}\cdot \frac{lg5}{lg4}\cdot ... \cdot \frac{lg8}{lg7} =}\\ \\ \mathtt{= \frac{lg8}{lg2}=log_28=log_22^3=3log_22=3 }\\ \\\mathtt{log_23 \cdot log_34\cdot log_45\cdot ... \cdot log_78=3}$