To find the zero of the function $f(x) = 3 - 2^x$, we need to solve the equation:

$f(x) = 0$

So, set $3 - 2^x = 0$ and solve for $x$:

$3 = 2^x$

Now, take the logarithm of both sides (we can use the natural logarithm or any logarithm base):

$\ln(3) = \ln(2^x)$

Using the logarithm power rule, $\ln(2^x) = x \ln(2)$:

$\ln(3) = x \ln(2)$

Finally, solve for $x$:

$x = \frac{\ln(3)}{\ln(2)}$

This is the exact value of $x$. To approximate it:

$x \approx \frac{1.0986}{0.6931} \approx 1.585$

So, the zero of the function $f(x) = 3 - 2^x$ is approximately $x \approx 1.585$.

Would you like any further details or have any questions?

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Here are 5 questions related to this topic:

1. What is the importance of finding the zero of a function in mathematical analysis?
2. How do different logarithmic bases affect the calculation of logarithms?
3. Can you find the zero for a similar function, such as $f(x) = 5 - 3^x$?
4. How can you verify the solution to $f(x) = 3 - 2^x$ using graphing techniques?
5. What is the significance of the natural logarithm in solving exponential equations?

Tip: When solving exponential equations, logarithms are powerful tools for simplifying expressions and finding solutions.