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
![**Solve for x:**
\[ \log_5 625 = x \]
Here is a step-by-step method to solve the equation:
1. First, recall the definition of a logarithm: \( \log_b a = c \) means \( b^c = a \).
2. Using the definition, we can rewrite the equation \( \log_5 625 = x \) as \( 5^x = 625 \).
Next, we need to determine what power of 5 equals 625:
- \( 5^2 = 25 \)
- \( 5^3 = 125 \)
- \( 5^4 = 625 \)
From the calculations, we can see that \( 5^4 = 625 \). Therefore, \( x = 4 \).
**Answer:**
\[ x = 4 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f516166-4390-4e41-acf6-d563f0703180%2F2bb3ce48-4288-4921-989f-5ed91555a8f8%2Faanv6yp_processed.png&w=3840&q=75)
Transcribed Image Text:**Solve for x:**
\[ \log_5 625 = x \]
Here is a step-by-step method to solve the equation:
1. First, recall the definition of a logarithm: \( \log_b a = c \) means \( b^c = a \).
2. Using the definition, we can rewrite the equation \( \log_5 625 = x \) as \( 5^x = 625 \).
Next, we need to determine what power of 5 equals 625:
- \( 5^2 = 25 \)
- \( 5^3 = 125 \)
- \( 5^4 = 625 \)
From the calculations, we can see that \( 5^4 = 625 \). Therefore, \( x = 4 \).
**Answer:**
\[ x = 4 \]
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