Math Problem Statement

3^x = 5^{2x}

Solution

To solve the equation 3x=52x3^x = 5^{2x}, let's work through it step by step.

  1. Take the natural logarithm of both sides: ln(3x)=ln(52x)\ln(3^x) = \ln(5^{2x})

  2. **

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Math Problem Analysis

Mathematical Concepts

Exponential Equations
Logarithms

Formulas

log_b(a^x) = x * log_b(a)
logarithmic properties

Theorems

Logarithmic Identity
Exponentiation Rules

Suitable Grade Level

Grades 10-12