Question

Determine the approximate solution to 2 times 3^x = 10

1.7
1.5
2
10

Answer 1

To solve the equation \( 2 \times 3^x = 10 \), we can first isolate the term with the exponent:

\[
3^x = \frac{10}{2} = 5
\]

Now, we take the logarithm of both sides to solve for \( x \):

\[
x \log(3) = \log(5)
\]

Now, solve for \( x \):

\[
x = \frac{\log(5)}{\log(3)}
\]

Now, we can calculate this using a calculator. Let’s substitute the values of \( \log(5) \) and \( \log(3) \):

- \( \log(5) \approx 0.6990 \)
- \( \log(3) \approx 0.4771 \)

So:

\[
x \approx \frac{0.6990}{0.4771} \approx 1.465
\]

Rounding this gives us approximately \( 1.5 \).

Thus, the approximate solution to the equation \( 2 \times 3^x = 10 \) is:

\[
\boxed{1.5}
\]