The expression you provided is: 

\[
2\log(x) - 4\log(y)
\]

We can simplify this expression using the properties of logarithms. Here are the steps:

1. **Apply the power rule** of logarithms, which states that \( a\log(b) = \log(b^a) \).

So:

\[
2\log(x) = \log(x^2)
\]
and
\[
4\log(y) = \log(y^4)
\]

2. Now, substitute these into the original expression:

\[
\log(x^2) - \log(y^4)
\]

3. **Use the subtraction rule** for logarithms: \( \log(a) - \log(b) = \log\left(\frac{a}{b}\right) \).

Thus, the expression becomes:

\[
\log\left(\frac{x^2}{y^4}\right)
\]

So, the simplified form of the given expression is:

\[
\log\left(\frac{x^2}{y^4}\right)
\]

If you'd like more details on any of the logarithmic properties or have additional questions, feel free to ask!

### Related questions:
1. How do logarithmic properties like the product rule or quotient rule work?
2. How can logarithms be used to solve equations involving exponents?
3. Can you explain the natural logarithm (\(\ln\)) and its properties?
4. What is the inverse relationship between logarithms and exponentials?
5. How do you solve logarithmic equations like \( \log(x) = 2 \)?

### Tip:
When simplifying logarithmic expressions, always remember to look for opportunities to apply the power, product, and quotient rules to condense them into simpler forms.

Learn how to simplify the expression 2log(x) - 4log(y) using logarithmic properties like the power rule and subtraction rule. This step-by-step guide is perfect for students in Grades 9-12 studying logarithms and simplifying expressions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation