Question

the exponetial equation 3^x=12 does not have an integer solutio round your solution to 2 decimal places
x=____ times ___ _____
answer blank 0 1 2 3 4 5 6 7 8 9

Answer 1

To solve the equation \( 3^x = 12 \) for \( x \), we can take the logarithm of both sides. Using the properties of logarithms, we have:

\[
x \log(3) = \log(12)
\]

Now solve for \( x \):

\[
x = \frac{\log(12)}{\log(3)}
\]

Using a calculator to evaluate the logs:

\[
\log(12) \approx 1.07918
\]
\[
\log(3) \approx 0.47712
\]

Now, divide:

\[
x \approx \frac{1.07918}{0.47712} \approx 2.26
\]

Rounding \( x \) to two decimal places gives:

\[
x \approx 2.26
\]

So, the value of \( x \) that solves the equation is approximately \( 2.26 \).

Now, filling in the blanks:

- \( x \) = **2** times **0** **.26**

This suggests that you could fill the blanks as follows based on the closest integer and the decimal part. You could choose various combinations; one way is:

- **2**
- **0**
- **26**

So the final answer would look like:

x = 2 times 0 26.