Question

Expand the logarithmic expression: log3 d/12

Answer 1

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: $\Rightarrow \log_3d-2\log_32-1$  

 

Answer 2

Answer:

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

Step-by-step explanation: