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Solved on Feb 03, 2024

Solve for $x$ without a calculator: $\frac{\ln x}{3} = 4$

STEP 1

Assumptions
1. The natural logarithm function is denoted as $\ln$ .
2. We are solving for the variable $x$ .
3. The equation to solve is $\frac{\ln x}{3} = 4$ .
4. We will use the properties of logarithms and exponential functions to solve for $x$ .

STEP 2

To isolate $\ln x$ , we need to eliminate the denominator. We can do this by multiplying both sides of the equation by 3.
$3 \cdot \frac{\ln x}{3} = 3 \cdot 4$

STEP 3

Simplify both sides of the equation.
$\ln x = 12$

STEP 4

To solve for $x$ , we need to get rid of the natural logarithm. We can do this by using the property that if $\ln a = b$ , then $a = e^b$ , where $e$ is the base of the natural logarithm.
$x = e^{12}$
$x = e^{12}$ is the solution to the equation $\frac{\ln x}{3} = 4$ .

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