Alaina257
Answered

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5. Solve [tex]$\log _6 60 - \log _6 30$[/tex].

A. [tex]$\log _6 2$[/tex]
B. [tex][tex]$\log _6 30$[/tex][/tex]
C. 2
D. 5

Sagot :

GinnyAnswer
To solve the expression [tex]\(\log_6 60 - \log_6 30\)[/tex], we can use the properties of logarithms. Specifically, the property that states:

[tex]\[ \log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right) \][/tex]

Applying this property:

[tex]\[ \log_6 60 - \log_6 30 = \log_6\left(\frac{60}{30}\right) \][/tex]

Now, simplify the fraction within the logarithm:

[tex]\[ \frac{60}{30} = 2 \][/tex]

Therefore, our expression now becomes:

[tex]\[ \log_6 \left(2\right) \][/tex]

This means the simplified form of [tex]\(\log_6 60 - \log_6 30\)[/tex] is:

[tex]\[ \log_6 2 \][/tex]

So, the correct answer is:

A. [tex]\(\log_6 2\)[/tex]
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