Math Problem Statement

Persamaan ^ 3 log(3x ^ 2 - x + 6) -^ 3 log(6x-9)=0 memiliki penyelesaian a dan b.

Solution

Untuk menyelesaikan persamaan log⁡3(3x2−x+6)−log⁡3(6x−9)=0\log_3(3x^2 - x + 6) - \log_3(6x - 9) = 0, kita dapat menggunakan sifat logaritma berikut:

log⁡ba−log⁡bc=log⁡b(ac)\log_b a - \log_b c = \log_b \left(\frac{a}{c}\right)

Maka persamaan tersebut dapat kita tulis ulang sebagai:

log⁡3(3x2−x+66x−9)=0\log_3 \left( \frac{3x^2 - x + 6}{6x - 9} \right) = 0

Diketahui bahwa log⁡b1=0\log_b 1 = 0. Jadi, untuk persamaan tersebut

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Math Problem Analysis

Mathematical Concepts

Logarithms
Equations

Formulas

Logarithm properties

Theorems

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Suitable Grade Level

High School

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