Question Number 164148 by mathlove last updated on 14/Jan/22
$${ln}\left(\frac{\mathrm{3}^{{x}} }{\frac{\mathrm{27}}{\mathrm{81}}}\right)=\mathrm{0}\:\:\:\:\:\:\:\:\:{then}\:\:\:\:{x}=? \\ $$
Answered by nikif99 last updated on 14/Jan/22
$$\mathrm{log}\:_{{b}} \mathrm{1}=\mathrm{0}\:\Rightarrow \\ $$$$\left(\frac{\mathrm{3}^{{x}} }{\frac{\mathrm{27}}{\mathrm{81}}}\right)=\mathrm{1}\:\Rightarrow\mathrm{3}^{{x}} =\frac{\mathrm{3}^{\mathrm{3}} }{\mathrm{3}^{\mathrm{4}} }\:\Rightarrow\mathrm{3}^{{x}} =\mathrm{3}^{−\mathrm{1}} \:\Rightarrow{x}=−\mathrm{1} \\ $$