I am not sure of it but I think the expression will be like this : log (26 • 35)
[tex] log(26 \times 35) \\by \: \: \: using \: \: \: the \: \: \: following \: \: \: rule \: \: \: of \: \: \: logarithm \\ log(x \times y) = log(x) + log(y) \: \: \: we \: \: \: have \\ log(26) + log(35) [/tex]
C. log (26) + log (35)
Hope it helps.
Do comment if you have any query.
Answer:
C. log (26) + log (35)
Step-by-step explanation:
Given expression:
[tex]\log(26 \cdot 35)[/tex]
To find which of the given answer options is equivalent to the given expression, apply log laws:
Option A
[tex]\textsf{Using the Quotient log law}: \quad \log_ax - \log_ay=\log_a\frac{x}{y}[/tex]
[tex]\implies \log 26 - \log 35=\log\left(\dfrac{26}{35}\right)[/tex]
Option B
[tex]\textsf{Using the Power log law}: \quad n\log_ax=\log_ax^n[/tex]
[tex]\implies 26 \cdot \log(35)=\log(35)^{26}[/tex]
Option C
[tex]\textsf{Using the Product log law}: \quad \log_ax + \log_ay=\log_axy[/tex]
[tex]\implies \log 26+\log 35 =\log(26 \cdot 35)[/tex]
Option D
No change:
[tex]\implies \log26 \cdot \log 35=\log26 \cdot \log 35[/tex]
Therefore, the expression that is equivalent to log (26 · 35) is option C.
Learn more about log laws here:
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