Math Problem Statement

8^{2}=64 write as logarithmic equation

Solution

The exponential equation 82=648^2 = 64 can be written as a logarithmic equation as follows:

log864=2\log_8 64 = 2

This reads as: "The logarithm of 64 with base 8 equals 2."

Would you like more details or have any questions about this conversion?

Here are 5 related questions for further exploration:

  1. What is the logarithmic form of 25=322^5 = 32?
  2. How do you simplify log28\log_2 8?
  3. Can you solve for xx in logx81=4\log_x 81 = 4?
  4. How do you express 103=100010^3 = 1000 as a logarithmic equation?
  5. What is the value of log10100\log_{10} 100?

Tip: The logarithmic form of an equation helps you solve for exponents, and it's especially useful when you need to find unknown powers.

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Math Problem Analysis

Mathematical Concepts

Exponents
Logarithms
Base Conversion

Formulas

Logarithmic form: b^x = y ⇔ log_b(y) = x

Theorems

Inverse Properties of Exponents and Logarithms

Suitable Grade Level

Grades 8-10