Question

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

Answer 1

Answer:

x = 0.598

Step-by-step 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

$4x-2=\frac{ln3}{(ln6+1)}\\\\4x=\frac{ln3}{(ln6+1)} + 2\\\\x = \frac{\frac{ln3}{(ln6+1)} + 2}{4}$

$x = \frac{\frac{ln3}{(ln6+1)} + 2}{4} \\\\x = 0.598$