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3 years ago

Expand the logarithmic expression: log3 d/12

Mathematics

2 answers:

Anni [7]3 years ago

6 0

Answer:

Expanded form: $\Rightarrow \log_3d-2\log_32-1$

Step-by-step explanation:

Given: $\log_3\dfrac{d}{12}$

Subtraction property of log: log a/b = log a - log b

Addition property of log: log(ab) = log a+ log b

$\log_aa=1$

$\log_ab^m=m\log_ab$

$\log_3\dfrac{d}{12}=\log_3d-\log_312$ (Subtraction property )

$\Rightarrow \log_3d-\log_3(4\times 3)$

$\Rightarrow \log_3d-(\log_34+\log_33)$ (Addition Property)

$\Rightarrow \log_3d-\log_34-\log_33$ (Distributive property)

$\Rightarrow \log_3d-\log_34-1$ ( $\log_aa=1$ )

$\Rightarrow \log_3d-2\log_32-1$

The expanded form of $\log_3\dfrac{d}{12}$ is

$\Rightarrow \log_3d-2\log_32-1$

Hence, Expanded form: $\Rightarrow \log_3d-2\log_32-1$

Temka [501]3 years ago

5 0

Answer:

log(base 3)(d/12) = log(base 3)d - log(base 3)12

Step-by-step explanation:

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