Math Problem Statement

In 3^50, 4^40, 5^30, and 6^20, which number is the largest?

Solution

The question in the image is asking:

"In 3^50, 4^40, 5^30, and 6^20, which number is the largest?"

Approach to solving:

We need to compare the values of 350,440,530,6203^{50}, 4^{40}, 5^{30}, 6^{20}. A direct computation can help, but instead of manually calculating these large numbers, we can compare their logarithmic values to make it easier.

We use logarithms to compare powers:

log(ab)=blog(a)\log(a^b) = b \log(a)

Thus, we'll calculate:

  1. 50log(3)50 \log(3)
  2. 40log(4)40 \log(4)
  3. 30log(5)30 \log(5)
  4. 20log(6)20 \log(6)

We'll then compare these values to determine the largest one.

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Logarithms
Comparative Analysis

Formulas

log(a^b) = b * log(a)

Theorems

Logarithmic Properties for Comparison of Exponents

Suitable Grade Level

Grades 9-12