To make \( x \) the subject of the equation \( y = \log_{10}(2x) \), follow these steps:

1. Start with the given equation:
   \[
   y = \log_{10}(2x)
   \]

2. Convert the logarithmic equation to its exponential form. Recall that if \( y = \log_{10}(A) \), then \( A = 10^y \). Applying this to the equation:
   \[
   2x = 10^y
   \]

3. Solve for \( x \) by dividing both sides by 2:
   \[
   x = \frac{10^y}{2}
   \]

So, the expression for \( x \) in terms of \( y \) is:
\[
x = \frac{10^y}{2}
\]

Would you like more details or have any questions?

Here are five related questions for further practice:
1. How would you solve for \( x \) if the equation were \( y = \log_{10}(3x + 1) \)?
2. What is the value of \( x \) if \( y = \log_{10}(2x) \) and \( y = 2 \)?
3. How do you convert a logarithmic equation to an exponential form?
4. What is the inverse function of \( y = \log_{10}(2x) \)?
5. How would the process differ if the equation were \( y = \ln(2x) \)?

**Tip:** When working with logarithmic equations, converting them to exponential form often simplifies the process of solving for the variable.

Learn how to make x the subject of the equation y = log10(2x) step-by-step with detailed explanations. This problem involves logarithms and exponential equations, suitable for advanced high school students. Practice solving similar equations to master logarithmic transformations.

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