Math Problem Statement
3 * (2 log(x+1) / log 3) = 2x + 1
Solution
The given equation is:
Let's solve this step by step:
Step 1: Simplify the equation
Multiply through by to eliminate the denominator:
Step 2: Rewrite the logarithm
Using the property of logarithms , rewrite :
Step 3: Exponentiate both sides
To eliminate the logarithms, exponentiate both sides with base 10:
Step 4: Expand and rearrange
Expand the left-hand side:
This is a transcendental equation (involves both and ), so we solve it numerically.
Step 5: Solve numerically
Using numerical methods (e.g., Newton's method), the solution is approximately:
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Math Problem Analysis
Mathematical Concepts
Logarithms
Transcendental Equations
Exponentiation
Formulas
a log b = log(b^a)
Exponentiation of logarithms: if log(a) = log(b), then a = b
Theorems
Properties of logarithms
Basic rules of exponential functions
Suitable Grade Level
Grades 11-12