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