Math Problem Statement

Evaluate log base 6 of 1.

Solution

The problem in the image is asking to evaluate:

log6(1)\log_6(1)

In general, for any logarithm logb(x)\log_b(x), it asks "to what power must the base bb be raised to give xx?"

In this case:

log6(1)=?\log_6(1) = ?

This expression is asking "to what power must 6 be raised to give 1?"

The answer is 00, because any non-zero number raised to the power of 0 equals 1:

60=16^0 = 1

Therefore:

log6(1)=0\log_6(1) = 0

Would you like more details on logarithmic properties or any related topics? Here are 5 related questions to explore:

  1. How do you evaluate logarithms with different bases?
  2. What are the properties of logarithms that can simplify expressions?
  3. How do logarithms relate to exponential functions?
  4. What is the change of base formula for logarithms?
  5. How can logarithms be applied in solving real-world problems?

Tip: Always remember that logb(1)\log_b(1) is 0 for any base b>0b > 0.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents

Formulas

log_b(x) = y if and only if b^y = x

Theorems

Logarithm identity: log_b(1) = 0 for any base b > 0

Suitable Grade Level

Grades 9-12