Math Problem Statement

3^(x-1)=2^(x+1)

Solution

We need to solve the equation:

3(x−1)=2(x+1)3^{(x-1)} = 2^{(x+1)}

Step 1: Take the natural logarithm on both sides

Applying the natural logarithm (ln) to both sides:

ln⁡(3(x−1))=ln⁡(2(x+1))\ln(3^{(x-1)}) = \ln(2^{(x+1)})

Using the logarithm power rule, ln⁡ab=bln⁡a\ln a^b = b \ln a, we rewrite it as:

[ (x-1) \ln 3 = (x+1) \ln 2 \

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Math Problem Analysis

Mathematical Concepts

Exponential Equations
Logarithms

Formulas

ln(a^b) = b * ln(a)

Theorems

Logarithmic Power Rule

Suitable Grade Level

Grades 9-11

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