The problem asks to find the missing values of $x$ in the table using the equation $y = 3 \times (10^x)$.

Let's first analyze the table and equation:

The equation is: $y = 3 \times 10^x$ This tells us that $y$ is 3 times 10 raised to the power of $x$. We can use this to solve for $x$ when $y$ is given and vice versa.

Table breakdown:

We need to find the values of $x$ for $y = 300$ and $y = 1503.56$.

Step-by-step solution:

1. For $y = 300$: $300 = 3 \times 10^x$ Dividing both sides by 3: $100 = 10^x$ Taking the logarithm base 10 of both sides: $x = \log_{10}(100) = 2$

2. For $y = 1503.56$: $1503.56 = 3 \times 10^x$ Dividing both sides by 3: $501.19 = 10^x$ Taking the logarithm base 10 of both sides: $x = \log_{10}(501.19) \approx 2.7$

Final table with missing $x$ values:

Would you like more details or have any other questions about this process?

Here are 5 related questions:

1. How does changing the base of the logarithm affect the calculation of $x$?
2. Can you derive the general form of the equation for any arbitrary $a$ in $y = a \times 10^x$?
3. How would you approach solving for $x$ if the equation was $y = 5 \times 10^x$ instead?
4. What if the base of the exponential term was $e$ instead of 10, how would you solve for $x$?
5. How would you use logarithmic properties to solve more complex exponential equations?

Tip: To solve exponential equations like $y = a \times b^x$, isolating the exponential term and then taking the logarithm of both sides is often the most efficient approach.