Math Problem Statement

log4(1/64)=−3 is equivalent in exponential form to . (DO NOT SIMPLIFY! DO NOT USE parentheses!)

Solution

The equation log4(164)=3\log_4\left(\frac{1}{64}\right) = -3 can be expressed in exponential form as:

43=1644^{-3} = \frac{1}{64}

If you have any questions or would like more details, feel free to ask! Here are some related questions you might consider:

  1. What are the properties of logarithms?
  2. How do you convert logarithmic equations to exponential form?
  3. Can you explain the significance of the base in logarithms?
  4. What other examples can you give of logarithmic to exponential conversions?
  5. How do you solve logarithmic equations?

Tip: Always remember that the base of the logarithm becomes the base of the exponent in the conversion!

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponential Functions

Formulas

log_b(a) = c ↔ b^c = a

Theorems

Logarithmic identities

Suitable Grade Level

Grades 7-10