Answer:
[tex]\log _2\left(9x\right)-\log _2\left(3\right)=3 : x = \frac{8}{3}[/tex]
Decimal:
[tex]x = 2.66666...[/tex]
Step-by-step explanation:
[tex]\log _2\left(9x\right)-\log _2\left(3\right)=3[/tex]
Add [tex]log _2\left(3)[/tex] to both sides:
[tex]\log _2\left(9x\right)-\log _2\left(3\right)+\log _2\left(3\right)=3+\log _2\left(3\right)[/tex]
Simplify:
[tex]\log _2\left(9x\right)=3+\log _2\left(3\right)[/tex]
Use the logarithmic definition: If [tex]\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c[/tex]
[tex]\log _2\left(9x\right)=3+\log _2\left(3\right)\quad \Rightarrow \quad \:9x=2^{3+\log _2\left(3\right)}[/tex]
[tex]9x=2^{3+\log _2\left(3\right)}[/tex]
Expand [tex]2^{3+\log _2\left(3\right)} : 24[/tex]
[tex]9x=24[/tex]
Solve: [tex]9x=24 : x = \frac{8}{3}[/tex]
[tex]x = \frac{8}{3}[/tex]
Verify solutions: [tex]x = \frac{8}{3}[/tex] : True
The solution is:
[tex]x=\frac{8}{3}[/tex]
Hope I helped. If so, may I get brainliest and a thanks?
Thank you, have a good day! =)
