https://file.aiquickdraw.com/mathbot/file/1726671839846awf7xsiq.jpg

The equation in the image is:

\[
\frac{\log{x}}{1 - \log{2}} = 2
\]

To solve for \( x \), follow these steps:

### Step 1: Isolate \(\log{x}\)
Multiply both sides by \( 1 - \log{2} \):

\[
\log{x} = 2(1 - \log{2})
\]

Simplify the right side:

\[
\log{x} = 2 - 2\log{2}
\]

### Step 2: Apply logarithmic properties
Use the property \( a\log{b} = \log{b^a} \) to simplify the second term on the right side:

\[
\log{x} = 2 - \log{2^2}
\]

Since \( 2^2 = 4 \), this becomes:

\[
\log{x} = 2 - \log{4}
\]

### Step 3: Combine the terms
Use the property \( \log{a} - \log{b} = \log{\frac{a}{b}} \) to combine the terms:

\[
\log{x} = \log{10^2} - \log{4}
\]

\[
\log{x} = \log{\frac{100}{4}}
\]

\[
\log{x} = \log{25}
\]

### Step 4: Solve for \( x \)
Since \(\log{x} = \log{25}\), we can conclude that:

\[
x = 25
\]

The solution is \( x = 25 \).

Would you like more details, or do you have any questions?

### Related Questions:
1. How do you apply logarithmic properties to simplify expressions?
2. What is the change of base rule for logarithms?
3. How can logarithmic equations be solved if the logarithms have different bases?
4. What are some common properties of logarithms useful for simplifying equations?
5. How do you solve an equation with logarithms involving multiplication or division?

**Tip:** Remember that logarithmic properties, such as the product, quotient, and power rules, are essential for solving complex logarithmic equations efficiently.

Solve the equation: (log x) / (1 - log 2) = 2

Learn how to solve the logarithmic equation (log x) / (1 - log 2) = 2 step-by-step, applying logarithmic properties such as power and quotient rules. This problem is suitable for students in Grades 10-12 and covers key algebra concepts.

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