M(x) = log10(x / 0.001)

7.7 = log10(x / 0.001)

10^7.7 = x / 0.001

x = 10^7.7 * 0.001

what is the result

To solve the equation \( x = 10^{7.7} \times 0.001 \), we follow these steps:

1. Calculate \( 10^{7.7} \):
\[ 10^{7.7} \approx 50118723.36 \]

2. Multiply this result by \( 0.001 \):
\[ x = 50118723.36 \times 0.001 \]
\[ x \approx 50118.72336 \]

Therefore, the result is approximately \( 50118.72336 \).

Would you like more details or have any questions about this solution? Here are 5 numbered questions you might consider asking:

1. How do logarithms work and what are their properties?
2. Can you explain how to convert from logarithmic to exponential form?
3. What are some common uses of logarithms in real-world applications?
4. How do you handle different bases in logarithms?
5. Can you explain the steps in solving logarithmic equations in more detail?

**Tip:** When dealing with logarithmic and exponential equations, it's helpful to remember that the base of the logarithm and the base of the exponential must match for the operations to be straightforward.

Learn how to solve the logarithmic equation M(x) = log10(x / 0.001) with a step-by-step solution. This problem involves logarithm properties and exponential functions, providing a detailed approach to find the solution. Suitable for students in Grades 10-12.

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