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777dan777 [17]
3 years ago
6

O log2 3x + log2 3=2

Mathematics
1 answer:
ipn [44]3 years ago
8 0

Answer:

\large\boxed{x=\dfrac{4}{9}}

Step-by-step explanation:

\log_23x+\log_23=2\\\\\bold{DOMAIN}:\\3x>0\to x>0\\\\\text{Use}\ \log_ab+\log_ac=\log_a(bc)\\\\\log_2\bigg[(3x)(3)\bigg]=2\\\\\log_29x=2\qquad\text{use}\ \log_ab=c\iff a^c=b\\\\\log_29x=\log_22^2\\\\\log_29x=\log_24\iff9x=4\qquad\text{divide both sides by 9}\\\\\dfrac{9x}{9}=\dfrac{4}{9}\\\\\boxed{x=\dfrac{4}{9}}\in \bold{DOMAIN}

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