Answer:
The equation 'log Subscript 3 Baseline (negative 2 x minus 3) = 2' i.e. [tex]\log _3\left(-2x-3\right)=2[/tex] has x = –6 as the solution.
Step-by-step explanation:
Checking the equation
log Subscript 3 Baseline (negative 2 x minus 3) = 2
Writing in algebraic expression
[tex]\log _3\left(-2x-3\right)=2[/tex]
Use the logarithmic definition
[tex]\mathrm{If}\:\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c[/tex]
[tex]\log _3\left(-2x-3\right)=2\quad \Rightarrow \quad \:-2x-3=3^2[/tex]
[tex]-2x-3=3^2[/tex]
[tex]-2x-3=9[/tex]
[tex]-2x=12[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-2[/tex]
[tex]\frac{-2x}{-2}=\frac{12}{-2}[/tex]
[tex]x=-6[/tex]
Therefore, the equation 'log Subscript 3 Baseline (negative 2 x minus 3) = 2' i.e. [tex]\log _3\left(-2x-3\right)=2[/tex] has x = –6 as the solution.
