Question

O log2 3x + log2 3=2

Answer 1

`\large\boxed{x=(4)/(9)}`

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}\\\\(9x)/(9)=(4)/(9)\\\\\boxed{x=(4)/(9)}\in \bold{DOMAIN}`