Math Problem Statement

Evaluate \( \log_3(27) \).

Solution

The exercise asks to evaluate the expression log3(27)\log_3(27).

Solution:

To evaluate log3(27)\log_3(27), we need to determine the power to which 3 must be raised to give 27.

We know that: 33=273^3 = 27

Therefore: log3(27)=3\log_3(27) = 3

So, the value of log3(27)\log_3(27) is 3.

Would you like more details or have any further questions?

Here are 5 related questions you might find useful:

  1. How do you calculate log3(81)\log_3(81)?
  2. What is the value of log5(25)\log_5(25)?
  3. How do you solve logarithmic equations such as logb(x)=n\log_b(x) = n?
  4. What is the relationship between logarithms and exponents?
  5. How can you convert a logarithmic expression to an exponential form?

Tip: Always remember that logarithms are the inverse of exponents. If logb(x)=y\log_b(x) = y, then by=xb^y = x.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents

Formulas

log_b(x) = y \Rightarrow b^y = x

Theorems

Inverse relationship between logarithms and exponents

Suitable Grade Level

Grades 9-10