Find the exact value log_3(30) -log _3(10)

We can simplify the given expression using logarithmic properties. The expression is:

\[
\log_3(30) - \log_3(10)
\]

Using the **logarithmic subtraction rule** (which states that \(\log_b(x) - \log_b(y) = \log_b\left(\frac{x}{y}\right)\)), we can combine the two logarithms:

\[
\log_3\left(\frac{30}{10}\right)
\]

Simplify \(\frac{30}{10}\):

\[
\log_3(3)
\]

Since \(\log_b(b) = 1\), we have:

\[
\log_3(3) = 1
\]

Thus, the exact value of the expression is:

\[
1
\]

Would you like any further details on this process or another question?

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1. What are the properties of logarithms?
2. How can logarithms be used to solve exponential equations?
3. Can you explain the change of base formula in logarithms?
4. What is the difference between natural logarithms and common logarithms?
5. How do you compute logarithms of numbers that are not powers of the base?

**Tip:** The logarithmic subtraction rule is particularly useful for simplifying complex expressions!

Find the exact value log_3(30) - log_3(10)

Understand how to solve log_3(30) - log_3(10) using the logarithmic subtraction rule. This step-by-step explanation demonstrates how to simplify the expression to log_3(3), which equals 1. Suitable for students in Grades 9-10.

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