Math Problem Statement

3 log 125 . 5 log 8 . 2 log 9

Solution

You have three logarithmic expressions:

  1. 3log1253 \log 125
  2. 5log85 \log 8
  3. 2log92 \log 9

Let's simplify each one individually:

1. 3log1253 \log 125

Using the logarithmic property alogb=logbaa \log b = \log b^a, we rewrite it as: 3log125=log1253=log19531253 \log 125 = \log 125^3 = \log 1953125

2. 5log85 \log 8

Again, applying alogb=logbaa \log b = \log b^a, we get: 5log8=log85=log327685 \log 8 = \log 8^5 = \log 32768

3. 2log92 \log 9

Using the same property: 2log9=log92=log812 \log 9 = \log 9^2 = \log 81

The final simplified expressions are: 3log125=log19531253 \log 125 = \log 1953125 5log8=log327685 \log 8 = \log 32768 2log9=log812 \log 9 = \log 81

Would you like to know more details or have any questions about logarithms or simplification?

Here are 5 related questions:

  1. What is the logarithmic property log(ab)\log(a \cdot b)?
  2. How would you simplify 4log164 \log 16?
  3. What is the value of log10\log 10 in base 10?
  4. How do you convert natural logarithms to base 10?
  5. How can logarithms be used to solve exponential equations?

Tip: Always remember the power rule of logarithms: alogb=logbaa \log b = \log b^a.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents
Algebra

Formulas

a log b = log b^a (Power Rule of Logarithms)

Theorems

Power Rule of Logarithms

Suitable Grade Level

Grades 9-12