Answer:
2
Step-by-step explanation:
Given expression:
[tex]\log_82+3\log_82+\dfrac{1}{2}\log_816[/tex]
[tex]\textsf{Apply the Power law}: \quad n\log_ax=\log_ax^n[/tex]
[tex]\implies \log_82+\log_82^3+\log_816^{\frac{1}{2}[/tex]
Simplify:
[tex]\implies \log_82+\log_88+\log_84[/tex]
[tex]\textsf{Apply the Product law}: \quad \log_ax + \log_ay=\log_axy[/tex]
[tex]\implies \log_88+\log_8(2 \cdot 4)[/tex]
[tex]\implies \log_88+\log_88[/tex]
[tex]\implies 2\log_88[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies 2 \cdot 1[/tex]
[tex]\implies 2[/tex]
