$$ \log1.5\frac{1\text{ }}{\log5} $$ $$  $$$$  $$

It seems like there was a formatting issue with your input. Could you please clarify the expression you're working with? Here's an assumption based on the partial expression you provided:

If you're trying to express something like $\log 1.5$ divided by $\log 5$, the correct mathematical expression would be:

\[
\frac{\log 1.5}{\log 5}
\]

This expression represents the logarithm of 1.5 in base 5 using the change of base formula. Here's how it works:

### Step-by-Step Explanation:

1. **Change of Base Formula**: 
   The formula for changing the base of a logarithm is:
   \[
   \log_b a = \frac{\log_c a}{\log_c b}
   \]
   where $ \log_b a $ is the logarithm of $ a $ with base $ b $, and $ c $ is a new base (commonly 10 or $ e $ for natural logarithms).

2. **Apply to Your Expression**:
   Here, $ \frac{\log 1.5}{\log 5} $ can be interpreted as $ \log_5 1.5 $, which means the logarithm of 1.5 with base 5.

### Simplification (If Required):
The expression $\log_5 1.5$ doesn't simplify further without a calculator since it’s a specific value.

If you meant something else, feel free to clarify, and I'll assist you further.

### Related Questions:
1. How can you approximate logarithmic values without a calculator?
2. What are the properties of logarithms when the base and the argument are fractions?
3. How does the change of base formula help in solving logarithmic problems?
4. Can you calculate logarithms for non-integer values easily?
5. What are some applications of logarithms in real-world scenarios?

### Tip:
When working with logarithmic expressions, always ensure that you understand the base of the logarithm you're dealing with. Changing the base using the appropriate formula can often make complex calculations simpler.

Learn how to solve the logarithmic expression $ \log 1.5 / \log 5 $. This page provides a step-by-step explanation of the change of base formula, which is used to convert logarithms between different bases. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation