Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Problem Statement:**
Evaluate the expression and reduce to simplest terms:
\[
\log 2^4 + \log 5^4 =
\]
**Answer Box:** [ ]
**Instructions:**
To solve this problem, use the properties of logarithms. Apply the power rule of logarithms: \(\log a^b = b \log a\), which allows us to simplify expressions involving logarithms of powers.
Then, use the addition rule: \(\log a + \log b = \log (a \cdot b)\).
**Example Solution:**
Given:
\[
\log 2^4 + \log 5^4
\]
Step 1: Apply the power rule:
\[
4 \log 2 + 4 \log 5
\]
Step 2: Factor out the common coefficient:
\[
4 (\log 2 + \log 5)
\]
Step 3: Use the addition rule:
\[
4 \log(2 \cdot 5) = 4 \log 10
\]
**Final Simplified Expression:**
\[
4 \log 10
\]
Since \(\log 10 = 1\) in base 10, the expression simplifies to \(4 \times 1 = 4\).
Therefore, the answer is:
**4**
After completing the problem, click on "Submit Question" to check your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f3023e4-e765-481d-a4cf-2667beaa33ac%2F15dc7e74-9dff-44e7-9dbe-4bbfb08b0bcf%2Fjbxldg.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Evaluate the expression and reduce to simplest terms:
\[
\log 2^4 + \log 5^4 =
\]
**Answer Box:** [ ]
**Instructions:**
To solve this problem, use the properties of logarithms. Apply the power rule of logarithms: \(\log a^b = b \log a\), which allows us to simplify expressions involving logarithms of powers.
Then, use the addition rule: \(\log a + \log b = \log (a \cdot b)\).
**Example Solution:**
Given:
\[
\log 2^4 + \log 5^4
\]
Step 1: Apply the power rule:
\[
4 \log 2 + 4 \log 5
\]
Step 2: Factor out the common coefficient:
\[
4 (\log 2 + \log 5)
\]
Step 3: Use the addition rule:
\[
4 \log(2 \cdot 5) = 4 \log 10
\]
**Final Simplified Expression:**
\[
4 \log 10
\]
Since \(\log 10 = 1\) in base 10, the expression simplifies to \(4 \times 1 = 4\).
Therefore, the answer is:
**4**
After completing the problem, click on "Submit Question" to check your answer.
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