Question

Solve the equation. Write the answer in terms of the natural logarithm. 5e^{0.2x}=6[/tex]

Answer 1

Answer:

• x = 5 ln 1.2

Step-by-step explanation:

• $5e^{0.2x}=6$
• $e^{0.2x}=6/5$
• $e^{0.2x}=1.2$
• $ln (e^{0.2x})= ln 1.2$
• 0.2x = ln 1.2
• x = 5 ln 1.2

Answer 2

Answer:

$\displaystyle \rm {x}=5 \ln \bigg(\frac{6}{5} \bigg) \: or \: 0.91(approx)$

Step-by-step explanation:

we are given a logarithmic equation

$\displaystyle {5e}^{0.2x} = 6$

we want to figure out x

remember that,

$\ln( {e}^{x} ) = x$

therefore to use the above formula with our given equation

divide both sides by 5:

$\displaystyle \frac{{5e}^{0.2x} }{5}= \frac{6}{5}$

$\displaystyle {e}^{0.2x} = \frac{6}{5}$

take In both sides:

$\displaystyle \ln({e}^{0.2x} )= \ln \bigg(\frac{6}{5} \bigg)$

by using the formula we acquire

$\displaystyle 0.2x= \ln \bigg(\frac{6}{5} \bigg)$

we can rewrite left hand side as fraction

$\displaystyle \frac{1}{5} x= \ln \bigg(\frac{6}{5} \bigg)$

multiply both sides by 5

$\displaystyle x=5 \ln \bigg(\frac{6}{5} \bigg)$

and we are done!