Math Problem Statement

log525=y

Solution

To solve the equation log525=y\log_5 25 = y, we can convert it from logarithmic form to exponential form:

5y=255^y = 25

We know that 25=5225 = 5^2, so:

5y=525^y = 5^2

Since the bases are the same, we can set the exponents equal to each other:

y=2y = 2

Thus, y=2y = 2.

Would you like more details or have any further questions?

Here are five related questions:

  1. How do you solve equations with logarithms of different bases?
  2. What is the logarithmic property for multiplying numbers inside a log function?
  3. How do you express log51\log_5 1 in terms of exponents?
  4. What is the inverse function of a logarithmic equation?
  5. How can you solve log5(5x)=3\log_5 (5x) = 3?

Tip: When solving logarithmic equations, converting between logarithmic and exponential forms is often a helpful approach.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents

Formulas

log_b(a) = c ↔ b^c = a

Theorems

Logarithmic-Exponential Relationship

Suitable Grade Level

Grades 9-12