M(x) = log10(x / 0.001)

7.4 = log10(x / 0.001)

10^7.4 = x / 0.001

x = 10^7.4 * 0.001

x =

Let's solve for \( x \) step by step:

Given the equation:
\[ M(x) = \log_{10}\left(\frac{x}{0.001}\right) \]

We have:
\[ 7.4 = \log_{10}\left(\frac{x}{0.001}\right) \]

Convert the logarithmic equation to an exponential equation:
\[ 10^{7.4} = \frac{x}{0.001} \]

Rewriting the right-hand side:
\[ 10^{7.4} = x \cdot 1000 \]

Solve for \( x \):
\[ x = \frac{10^{7.4}}{1000} \]

Calculate \( 10^{7.4} \):
\[ 10^{7.4} \approx 2.51188643150958 \times 10^7 \]

Now divide by 1000:
\[ x = \frac{2.51188643150958 \times 10^7}{1000} \]
\[ x = 2.51188643150958 \times 10^4 \]
\[ x \approx 25118.8643150958 \]

So, the value of \( x \) is approximately:
\[ x \approx 25118.86 \]

Would you like more details or have any questions about the solution?

Here are 5 more questions you can ask:
1. How do you solve logarithmic equations involving different bases?
2. Can you explain the properties of logarithms?
3. What are common logarithm and natural logarithm, and how do they differ?
4. How do you graph logarithmic functions?
5. What are the applications of logarithms in real life?

**Tip:** When solving logarithmic equations, always consider converting them to their exponential form to simplify the calculations.

Learn how to solve the logarithmic equation 7.4 = log10(x / 0.001) step-by-step. Understand the conversion to exponential form and calculation of logarithms. Suitable for advanced high school and college students.

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