Question

Solve the equation. Write the answer in terms of the natural logarithm.

5e^{0.2x}=6[/tex]

Answer 1

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

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}= (6)/(5)`

`\displaystyle {e}^(0.2x) = (6)/(5)`

take In both sides:

`\displaystyle \ln({e}^(0.2x) )= \ln \bigg((6)/(5) \bigg)`

by using the formula we acquire

`\displaystyle 0.2x= \ln \bigg((6)/(5) \bigg)`

we can rewrite left hand side as fraction

`\displaystyle (1)/(5) x= \ln \bigg((6)/(5) \bigg)`

multiply both sides by 5

`\displaystyle x=5 \ln \bigg((6)/(5) \bigg)`

and we are done!

Answer 2

• x = 5 ln 1.2

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