Question Number 84000 by byaw last updated on 08/Mar/20
Commented by Kunal12588 last updated on 08/Mar/20
$${log}\:\sqrt[{\mathrm{3}}]{\mathrm{0}.\mathrm{0005957}}\:{should}\:{be}\:−{ve}\:? \\ $$
Answered by MJS last updated on 08/Mar/20
$$\mathrm{log}_{{b}} \:\mathrm{5}.\mathrm{957}\:=.\mathrm{7750} \\ $$$$\Leftrightarrow \\ $$$$\mathrm{5}.\mathrm{957}={b}^{.\mathrm{7750}} \\ $$$$\sqrt[{\mathrm{3}}]{\frac{\mathrm{5}.\mathrm{957}}{\mathrm{10000}}}={b}^{{x}} \\ $$$${x}=\frac{\mathrm{ln}\:\sqrt[{\mathrm{3}}]{\frac{\mathrm{5}.\mathrm{957}}{\mathrm{10000}}}}{\mathrm{ln}\:{b}}=\frac{\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{ln}\:\mathrm{5}.\mathrm{957}\:−\mathrm{4ln}\:\mathrm{10}\right)}{\mathrm{ln}\:{b}}= \\ $$$$=\frac{\mathrm{1}}{\mathrm{3}}\left(\frac{\mathrm{ln}\:\mathrm{5}.\mathrm{957}}{\mathrm{ln}\:{b}}−\frac{\mathrm{4ln}\:\mathrm{10}}{\mathrm{ln}\:{b}}\right)=\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{log}_{{b}} \:\mathrm{5}.\mathrm{957}\:−\mathrm{4log}_{{b}} \:\mathrm{10}\right)= \\ $$$$=\frac{\mathrm{1}}{\mathrm{3}}\left(.\mathrm{7750}−\mathrm{4log}_{{b}} \:\mathrm{10}\right)= \\ $$$$\:\:\:\:\:\left[{b}^{.\mathrm{7750}} =\mathrm{5}.\mathrm{957}\:\Rightarrow\:{b}\approx\mathrm{10}\right] \\ $$$$=−\mathrm{1}.\mathrm{075} \\ $$