Math Problem Statement

Find the cube root of log 9.

Solution

The equation in the image appears to be:

log93\sqrt[3]{\log 9}

This represents the cube root of the logarithm of 9. To solve this, we will assume the logarithm is in base 10 unless specified otherwise.

Steps:

  1. Find log9\log 9: Using base 10 logarithms: log1090.9542\log_{10} 9 \approx 0.9542

  2. Take the cube root: Now, calculate the cube root of this result: 0.954230.9836\sqrt[3]{0.9542} \approx 0.9836

Thus, the value of log930.9836\sqrt[3]{\log 9} \approx 0.9836.

Would you like more details on logarithms, or do you have any questions?

Here are 5 related questions:

  1. What are logarithmic properties that simplify expressions like log9\log 9?
  2. How would the result change if the logarithm was in a different base, such as base 2?
  3. What are the methods to calculate cube roots without a calculator?
  4. How does the logarithm of a product (e.g., log(3×3)\log(3 \times 3)) work in this context?
  5. How can you approximate logarithms manually?

Tip: Understanding logarithmic properties like the change of base rule can help solve a variety of logarithmic expressions quickly.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Cube Roots

Formulas

log_b(x) = y, where b^y = x
Cube Root: \( \sqrt[3]{x} \)

Theorems

Properties of Logarithms
Cube Root Theorem

Suitable Grade Level

Grades 9-12