The expression you provided is:

\[
5 \log 49
\]

Using logarithmic properties, you can factor out the constant 5:

\[
5 \log 49 = \log(49^5)
\]

Now, calculate \( 49^5 \):

\[
49^5 = (7^2)^5 = 7^{10}
\]

So the expression simplifies to:

\[
5 \log 49 = \log(7^{10}) = 10 \log 7
\]

Hence, \( 5 \log 49 = 10 \log 7 \).

If you need the decimal value of \( \log 7 \), we can approximate it:

\[
\log 7 \approx 0.8451
\]

Thus,

\[
5 \log 49 \approx 10 \times 0.8451 = 8.451
\]

Would you like further details or have any questions?

Here are 5 related questions you might find useful:
1. What are the properties of logarithms?
2. How does the change of base formula work in logarithms?
3. How do you simplify expressions with logarithmic exponents?
4. What is the relationship between natural logs and common logs?
5. How can logarithms be used to solve exponential equations?

**Tip:** Always remember that logarithms help simplify exponential expressions by turning multiplication into addition and powers into multiplication.

Discover how to simplify the expression 5 log 49 using logarithmic properties. This detailed explanation covers exponentiation and the logarithmic power rule, breaking the problem down step-by-step. Ideal for high school students studying logarithms and their applications.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation