Question

Solve. Round your answer to the nearest tenth. z

2^2 =264.950495290000

z=

Answer 1

To solve for \( z \) in the equation \( 2^z = 264.95049529 \), we can use logarithms.

First, we take the logarithm of both sides. You can use any logarithm, but for simplicity, we will use base 10 (common logarithm):

\[
\log(2^z) = \log(264.95049529)
\]

Using the property of logarithms that states \( \log(a^b) = b \cdot \log(a) \), we can simplify the left side:

\[
z \cdot \log(2) = \log(264.95049529)
\]

Now we can solve for \( z \):

\[
z = \frac{\log(264.95049529)}{\log(2)}
\]

Next, we calculate the values:

1. Calculate \(\log(264.95049529)\):
- Using a calculator, \(\log(264.95049529) \approx 2.423\)

2. Calculate \(\log(2)\):
- \(\log(2) \approx 0.301\)

Now substitute these values into the equation:

\[
z = \frac{2.423}{0.301} \approx 8.06
\]

Finally, rounding to the nearest tenth:

\[
z \approx 8.1
\]

Thus, the final answer is:

\[
\boxed{8.1}
\]