DavidCopperfield
Answered

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Given that log 2 = 0.3010 and log 3 = 0.4771 , how can we find log 6 ? ​

Sagot :

KiyotakaAyanokoji

Step-by-step explanation:

log 6 = log (2×3) = log 2 + log 3 = 0.3010+0.4771

=0.7781

semsee45

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]

Learn more about logarithm laws here:

https://brainly.com/question/27953288

https://brainly.com/question/27963321

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