Question

the exponetial equation 3^x=12 does not have an integer solutio round your solution to 2 decimal places
x= ____ times ____ _____

Answer 1

I dont think you understood x=____ times ___ _____ answer blank 0 1 2 3 4 5 6 7 8 9

Answer 2

To solve the exponential equation \(3^x = 12\), we can take the logarithm of both sides. Using the natural logarithm (ln) gives us:

\[
\ln(3^x) = \ln(12)
\]

By using the logarithmic identity \(\ln(a^b) = b \cdot \ln(a)\), we can rewrite the left side:

\[
x \cdot \ln(3) = \ln(12)
\]

Now, we can solve for \(x\):

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

Next, we can calculate this using logarithm values:

1. \(\ln(12) \approx 2.4849\)
2. \(\ln(3) \approx 1.0986\)

Now, we can divide these values:

\[
x \approx \frac{2.4849}{1.0986} \approx 2.26
\]

Rounded to two decimal places, we find:

\[
x \approx 2.26
\]

Thus, the answer to your question is:

\(x = 2.26\) times \(1\) (since it does not multiply by any other number in this specific context).

So, written in the requested format:

\(x = 2.26 \, \text{times} \, 1\)