Answer:
[tex]\sf \log_{10}6=0.7781[/tex]
Step-by-step explanation:
Given:
[tex]\sf \log_{10} 2 = 0.3010[/tex]
[tex]\sf \log_{10} 3 = 0.4771[/tex]
To find log₁₀ 6, first rewrite 6 as 3 · 2:
[tex]\sf \implies \log_{10}6=\log_{10}(3 \cdot 2)[/tex]
[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \sf \log_{10}(3 \cdot 2)=\log_{10}3+\log_{10}2[/tex]
Substituting the given values for log₁₀ 3 and log₁₀ 2:
[tex]\begin{aligned} \sf \implies \log_{10}3+\log_{10}2 & = \sf 0.4771+0.3010\\ & = \sf 0.7781 \end{aligned}[/tex]
Therefore:
[tex]\sf \log_{10}6=0.7781[/tex]
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