Question

5e^0.2x=7

Transformations of functions
ANSWERED
asked 2021-06-30
\(\displaystyle{5}{e}^{{0.2}}{x}={7}\)

Answers (1)

2021-07-01
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: \(\displaystyle{x}=\frac{{\ln{{1.4}}}}{{0.2}}\sim{0.477}\)
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