Question

Find the value of $lo{g}_{3}4.lo{g}_{4}5.lo{g}_{5}6.lo{g}_{6}7.lo{g}_{7}8.lo{g}_{8}9$.

• A. 2

Answer 1

The correct option is A 2

$lo{g}_{3}4.lo{g}_{4}5.lo{g}_{5}6.lo{g}_{6}7.lo{g}_{7}8.lo{g}_{8}9$

Using change of base identity, $lo{g}_{b}a=\frac{lo{g}_{m}a}{lo{g}_{m}b}$ and taking common base as 10, we get

$\frac{log4}{log3}.\frac{log5}{log4}.\frac{log6}{log5}.\frac{log7}{log6}.\frac{log8}{log7}.\frac{log9}{log8}$

$=\frac{log9}{log3}$

$=\frac{log9}{log3}=\frac{log{3}^2}{log3}=2\times \frac{log3}{log3}=2$