Evaluate the expression without using a calculator.
18)

To evaluate the expression , we can use the property of logarithms and exponentials that states . This allows us to simplify our expression directly.

So, applying this property:

Thus, the final answer is .

Now, let’s dig a bit deeper into our topic!

Using logarithmic and exponential functions is not just for academics; they’re crucial in fields like finance for analyzing compound interest or in biology for understanding population growth. These relationships help professionals make informed decisions based on growth predictions and time value of money.

Remember, when dealing with logarithmic identities, a common misstep is forgetting to apply the arguments correctly. For instance, mixing up with can lead to confusion as they yield different results. Always double-check where your constants are headed!