Math Problem Statement

The original handwritten problem shows the expressions \(\log_5 125\) and \(\log_2 8 = 3\).

Solution

The image contains mathematical expressions written in Arabic script, which translate to:

  1. log5125\log_5 125
  2. log28=3\log_2 8 = 3

Explanation:

  1. The first expression is log5125\log_5 125. To solve this, we find the power to which 5 must be raised to get 125. Since 53=1255^3 = 125, log5125=3\log_5 125 = 3.
  2. The second expression, log28=3\log_2 8 = 3, is already simplified. It states that the power to which 2 must be raised to get 8 is 3, since 23=82^3 = 8.

Would you like more details or have any questions?

Related Questions:

  1. What are the properties of logarithms?
  2. How do you convert between logarithmic and exponential forms?
  3. What are the laws of logarithms, such as the product, quotient, and power rules?
  4. How can you solve logarithmic equations with different bases?
  5. What are common logarithms and natural logarithms, and how are they used?

Tip: Always remember that logba=c\log_b a = c is equivalent to bc=ab^c = a. This helps in converting between logarithmic and exponential forms.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Logarithms
Exponential Functions

Formulas

\(\log_b a = c\) is equivalent to \(b^c = a\)
Simplifying logarithmic expressions

Theorems

Logarithmic and Exponential Relationship

Suitable Grade Level

Grades 8-10