Question

# 5e^0.2x=7

Transformations of functions
$$\displaystyle{5}{e}^{{0.2}}{x}={7}$$

We are given: $$\displaystyle{5}{e}^{{0.2}}{x}={7}$$
Divide both sides by 5: $$\displaystyle{e}^{{0.2}}{x}={1.4}$$
Take the natural logarithm of both sides: $$\displaystyle{{\ln{{e}}}^{{0.2}}{x}}={\ln{{1.4}}}$$
Use the rule: $$\displaystyle{{\ln{{e}}}^{{x}}=}{x}$$ $$\displaystyle{0.2}={\ln{{1.4}}}$$
Divide both sides by 0.2: $$\displaystyle{x}=\frac{{\ln{{1.4}}}}{{0.2}}\sim{0.477}$$