Answer:
[tex] \displaystyle \rm {x}=5 \ln \bigg(\frac{6}{5} \bigg) \: or \: 0.91(approx)[/tex]
Step-by-step explanation:
we are given a logarithmic equation
[tex] \displaystyle {5e}^{0.2x} = 6[/tex]
we want to figure out x
remember that,
[tex] \ln( {e}^{x} ) = x[/tex]
therefore to use the above formula with our given equation
divide both sides by 5:
[tex] \displaystyle \frac{{5e}^{0.2x} }{5}= \frac{6}{5} [/tex]
[tex] \displaystyle {e}^{0.2x} = \frac{6}{5} [/tex]
take In both sides:
[tex] \displaystyle \ln({e}^{0.2x} )= \ln \bigg(\frac{6}{5} \bigg)[/tex]
by using the formula we acquire
[tex] \displaystyle 0.2x= \ln \bigg(\frac{6}{5} \bigg)[/tex]
we can rewrite left hand side as fraction
[tex] \displaystyle \frac{1}{5} x= \ln \bigg(\frac{6}{5} \bigg)[/tex]
multiply both sides by 5
[tex] \displaystyle x=5 \ln \bigg(\frac{6}{5} \bigg)[/tex]
and we are done!
