Question

Use natural logarithms to solve the equation.round to the nearest thousandth 6e^4x-2=3

Answer 1

x = 0.598

Explanation:

`6e^(4x-2) = 3`

Taking natural log on both sides

`ln(6e^(4x-2)) = ln(3)`

(4x-2) ln(6e) = ln(3)

(4x-2) (ln(6) + ln(e)) = ln3 //ln(e) = 1

(4x-2) (ln(6) + 1) = ln3

`4x-2=(ln3)/((ln6+1))\\\\4x=(ln3)/((ln6+1)) + 2\\\\x = ((ln3)/((ln6+1)) + 2)/(4)`

`x = ((ln3)/((ln6+1)) + 2)/(4) \\\\x = 0.598`