Questions: Question 10 1 pts IF ln x = 3/2, then x = e^(3/2) x = e^(2/3) x = (3/2) e x = (ln 3)/(ln 2)

Transcript text: Question 10 1 pts IF $\ln x=\frac{3}{2}$, then $x=e^{\frac{3}{2}}$ $x=e^{\frac{2}{3}}$ $x=\frac{3}{2} e$ $x=\frac{\ln 3}{\ln 2}$

Solution

Solution Steps

To solve for $ x $ given the equation $ \ln x = \frac{3}{2} $, we need to use the property of logarithms that states if $ \ln x = y $, then $ x = e^y $.

Solution Approach

Recognize that $ \ln x = \frac{3}{2} $ can be rewritten using the exponential function.
Use the property $ x = e^y $ where $ y = \frac{3}{2} $.

Step 1: Given Equation

We start with the equation given in the problem: \[ \ln x = \frac{3}{2} \]

Step 2: Exponential Form

Using the property of logarithms, we can rewrite the equation in exponential form: \[ x = e^{\frac{3}{2}} \]

Step 3: Calculate the Value

Calculating $ e^{\frac{3}{2}} $ gives us: \[ x \approx 4.4817 \]

Final Answer

Thus, the value of $ x $ is approximately: \[ \boxed{x \approx 4.4817} \]

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