Math Problem Statement

Solve the equation 5 log 25 = 2

Solution

The equation in the image is:

5log25=25 \log 25 = 2

Let's solve this step by step:

  1. Start by isolating the logarithmic term: log25=25\log 25 = \frac{2}{5}

  2. Convert the logarithmic equation to its exponential form: The logarithm log25\log 25 is typically base 10, so we write: 25=102525 = 10^{\frac{2}{5}}

  3. To simplify 102510^{\frac{2}{5}}, we can use the property of exponents: 1025=(102)15=1001510^{\frac{2}{5}} = (10^2)^{\frac{1}{5}} = 100^{\frac{1}{5}}

    The fifth root of 100 is approximately: 100152.511100^{\frac{1}{5}} \approx 2.511

Since the left-hand side of the original equation was 25, and 102510^{\frac{2}{5}} approximately equals 2.511, the equation as written is not exactly true. There might be a typo in the original problem.

Would you like more details or clarifications on this?

Here are 5 related questions:

  1. How do you convert logarithmic equations to exponential form?
  2. What is the difference between common and natural logarithms?
  3. How do you solve logarithmic equations with different bases?
  4. What are the properties of logarithms that can help simplify calculations?
  5. How do fractional exponents relate to roots?

Tip: When solving logarithmic equations, always make sure you correctly identify the base of the logarithm, which is typically 10 (common logarithm) or ee (natural logarithm).

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Math Problem Analysis

Mathematical Concepts

Logarithms
Algebra
Exponential Equations

Formulas

log_b(x) = y implies b^y = x
logarithm properties: log(x^n) = n*log(x)

Theorems

Exponential and Logarithmic Relationship

Suitable Grade Level

Grades 10-12