Question Number 10131 by konen last updated on 26/Jan/17
$$\mathrm{2}^{\mathrm{a}} =\mathrm{9} \\ $$$$\mathrm{27}^{\mathrm{b}} =\mathrm{8} \\ $$$$\Rightarrow\mathrm{a}×\mathrm{b}=? \\ $$
Answered by prakash jain last updated on 26/Jan/17
$$\mathrm{2}^{{a}} =\mathrm{9}\Rightarrow\mathrm{2}^{{a}} =\mathrm{3}^{\mathrm{2}} \:\:\:\:\:\left({A}\right) \\ $$$$\mathrm{27}^{{b}} =\mathrm{8}\Rightarrow\left(\mathrm{3}^{\mathrm{3}} \right)^{{b}} =\mathrm{2}^{\mathrm{3}} \Rightarrow\left(\mathrm{3}^{{b}} \right)^{\mathrm{3}} =\mathrm{2}^{\mathrm{3}} \Rightarrow\mathrm{3}^{{b}} =\mathrm{2}\:\left({B}\right) \\ $$$${substituting},\:\mathrm{2}=\mathrm{3}^{{b}} \:\mathrm{in}\:\left({A}\right) \\ $$$$\left(\mathrm{3}^{{b}} \right)^{{a}} =\mathrm{3}^{\mathrm{2}} \Rightarrow\mathrm{3}^{{ab}} =\mathrm{3}^{\mathrm{2}} \Rightarrow{ab}=\mathrm{2} \\ $$