Questions: Let f(x)=(4.5)^x Find x such that f(x)=528.38 Round your final answer to two decimal places?

Solution Steps

To find \( x \) such that \( f(x) = 528.38 \) for the function \( f(x) = (4.5)^x \), we need to solve the equation \( (4.5)^x = 528.38 \). This can be done by taking the logarithm of both sides and then solving for \( x \).

We start with the function defined as \( f(x) = (4.5)^x \) and set it equal to the given value:

\[ (4.5)^x = 528.38 \]

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

\[ \log((4.5)^x) = \log(528.38) \]

Using the property of logarithms, we can simplify the left side:

\[ x \cdot \log(4.5) = \log(528.38) \]

Now, we isolate \( x \):

\[ x = \frac{\log(528.38)}{\log(4.5)} \]

Calculating the values gives us:

\[ x \approx 4.1685 \]

Rounding this to two decimal places, we find:

\[ x \approx 4.17 \]

Final Answer