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
Never thought id have to say this but only one number per blank you had a problem with that last time and the website is having issues

Answer 1

To solve the equation \( 3^x = 12 \), we take the logarithm of both sides:

\[
x = \log_3(12)
\]

Using the change of base formula:

\[
x = \frac{\log_{10}(12)}{\log_{10}(3)} \quad \text{or} \quad x = \frac{\ln(12)}{\ln(3)}
\]

Calculating this using base 10 logarithms:

\[
\log_{10}(12) \approx 1.07918 \quad \text{and} \quad \log_{10}(3) \approx 0.47712
\]

Now we can calculate \( x \):

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

Rounding to two decimal places, we get:

\[
x \approx 2.26
\]

Thus, the final answer can be separated into its components:

- First blank: 2
- Second blank: 2
- Third blank: 6

So, you would fill in the blanks as follows:

\( x = \) 2 times 2 6