Math Problem Statement

4log3+4log8

Solution

The expression 4log3+4log84 \log 3 + 4 \log 8 can be simplified using the logarithmic property:

alogb=logbaa \log b = \log b^a

Step 1: Apply the logarithmic property to both terms

4log3=log34=log814 \log 3 = \log 3^4 = \log 81 4log8=log84=log40964 \log 8 = \log 8^4 = \log 4096

Step 2: Add the logarithms

Using the property loga+logb=log(ab)\log a + \log b = \log (a \cdot b), we can combine the two logarithms:

log81+log4096=log(81×4096)=log331776\log 81 + \log 4096 = \log (81 \times 4096) = \log 331776

Thus, the simplified expression is:

log331776\log 331776

Would you like further details on logarithmic properties or how to solve different forms of logarithmic expressions?

Here are 5 related questions you can try:

  1. Simplify 3log5+2log73 \log 5 + 2 \log 7.
  2. Solve log(2x)+log(3y)=log18\log (2x) + \log (3y) = \log 18.
  3. Simplify 2log4+3log62 \log 4 + 3 \log 6.
  4. Solve log5x=2\log 5x = 2.
  5. Simplify loga+logblogc\log a + \log b - \log c.

Tip: Always look for opportunities to apply logarithmic properties like product, quotient, and power rules to simplify expressions.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Algebra

Formulas

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

Theorems

Logarithmic Power Rule
Logarithmic Addition Rule

Suitable Grade Level

Grades 9-12