Question

What is the solution to the equation e^3x=12 Round your answer to the nearest hundredth

Answer 1

Answer:

.83 A

Step-by-step explanation:

Answer 2

Keywords:

equation, variable, clear, round, centesima, neperian logarithm, exponential

For this case we have the following equation $e ^ {3x} = 12$, from which we must clear the value of the variable "x" and round to the nearest hundredth. To do this, we must apply properties of neperian and exponential logarithms. By definition:

$ln (e ^ x) = x$

So:

$e ^ {3x} = 12$ We apply Neperian logarithm to both sides:

$ln (e^{3x}) = ln (12)\\3x = ln (12)$

We divide between "3" both sides of the equation:

$\frac {3x} {3} = \frac {ln (12)} {3}\\x = \frac {ln (12)} {3}\\x = 0.828302217$

Rounding out the nearest hundredth we have:

$x = 0.83$

Answer:

$x = 0.83$