## University Calculus: Early Transcendentals (3rd Edition)

$$t=4\ln^2 x$$
Another method to solve these exercises is to take the natural logarithm of both sides. In other words: $$e^x=a\hspace{1cm}\text{then}\hspace{1cm}\ln e^{x}=\ln a\hspace{1cm}\text{then}\hspace{1cm} x=\ln a$$ $$e^{\sqrt t}=x^2$$ - Take the natural logarithm of both sides: $$\ln(e^{\sqrt t})=\ln(x^2)$$ $$\sqrt t=\ln(x^2)$$ - Apply Power Rule: $$\sqrt t=2\ln x$$ $$t=(2\ln x)^2=4\ln^2 x$$