Math Problem Statement

solve log_ab/

Solution

To solve logab\log_a b, this expression represents the logarithm of bb to the base aa. Specifically, it asks, "To what power must aa be raised to get bb?"

The general formula for logarithms is:

logab=lnblna\log_a b = \frac{\ln b}{\ln a}

Here, ln\ln is the natural logarithm (logarithm with base ee).

Example:

If log28\log_2 8 is the question, we are looking for the power to which 2 must be raised to get 8:

\log_2 8 = 3 \quad \text{(since 2^3 = 8)}.

Would you like a specific example or a different logarithmic expression solved?


Here are 5 related questions:

  1. What is the value of log381\log_3 81?
  2. How do you solve log525\log_5 25?
  3. What is the result of log749\log_7 49?
  4. How do you calculate log101000\log_{10} 1000?
  5. Can you solve log232\log_2 32?

Tip: Logarithmic properties are useful for simplifying expressions, such as the power rule: loga(xn)=nlogax\log_a (x^n) = n \log_a x.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents
Algebra

Formulas

Logarithm formula: log_a b = ln(b) / ln(a)

Theorems

Change of Base Theorem

Suitable Grade Level

Grades 9-12