Answer
$$t=4\ln^2 x$$
Work Step by Step
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: $$\sqrt t=2\ln x$$ $$t=(2\ln x)^2=4\ln^2 x$$
