Math Problem Statement

Solve the expression: 20^2 / sqrt(ln(1.6 + 1.33) + 0.67 * ln(ln(1.6 + 1.33))).

Solution

It seems like you have shared an equation written on paper. I'll go ahead and transcribe the formula for further clarification.

From the image, it looks like the expression is:

202ln(1.6+1.33)+0.67ln(ln(1.6+1.33))\frac{20^2}{\sqrt{\ln(1.6 + 1.33) + 0.67 \ln(\ln(1.6 + 1.33))}}

Here’s a breakdown:

  • The numerator is 20220^2, which equals 400.
  • The denominator involves a square root (\sqrt{}) of a natural logarithmic expression:
    • ln(1.6+1.33)\ln(1.6 + 1.33) is inside the first part.
    • 0.67ln(ln(1.6+1.33))0.67 \ln(\ln(1.6 + 1.33)) is added to the result of the first log operation.

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Math Problem Analysis

Mathematical Concepts

Exponents
Square Root
Natural Logarithms

Formulas

Exponential formula: a^2
Square root: sqrt(x)
Natural logarithm: ln(x)

Theorems

Properties of logarithms
Properties of exponents and roots

Suitable Grade Level

Grades 10-12