Math Problem Statement

Write the expression log(2) + log(x) as a single logarithm. Assume that variables represent positive numbers.

Solution

The expression provided is:

log(2)+log(x)\log(2) + \log(x)

Using the logarithmic property that states:

log(a)+log(b)=log(ab)\log(a) + \log(b) = \log(a \cdot b)

The expression can be rewritten as a single logarithm:

log(2x)\log(2 \cdot x)

So, the answer is:

log(2x)\log(2x)

Let me know if you'd like a further explanation or have any other questions!

Here are 5 related questions for deeper understanding:

  1. How would you simplify log(a)log(b)\log(a) - \log(b)?
  2. What is the expanded form of log(x2)\log(x^2)?
  3. Can log(ab)\log(a \cdot b) be split into two logarithms?
  4. What is the base of the logarithm used here if it’s not specified?
  5. How do logarithmic rules apply to division, such as log(x)log(y)\log(x) - \log(y)?

Tip: Always double-check if the logarithmic expression is asking for simplification or expansion to apply the appropriate rule.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Simplification of Logarithmic Expressions

Formulas

log(a) + log(b) = log(a * b)

Theorems

Properties of Logarithms

Suitable Grade Level

Grades 9-12