For this case we must find the value of the variable "x" of the following expression:
[tex]4(10^{5x})=200[/tex]
We divide both sides of the equation by 4:
[tex]10 ^ {5x} = \frac {200} {4}\\10 ^ {5x} = 50[/tex]
We find ln on both sides of the equation to remove the exponent variable:
[tex]ln (10^{5x}) = ln (50)\\5x * ln (10) = ln (50)[/tex]
We divide both sides of the equation between 5 * ln (10):[tex]x = \frac {ln (50)} {5 * ln (10)}[/tex]
In decimal form we have:
[tex]x = 0.33979400[/tex]
ANswer:
[tex]x = 0.33979400[/tex]
