Respuesta :
Answer:
Option 1 - [tex]\log_{2}(9 {x}^{3} )=\log_{2}(9 ) +3 \log_{2}( {x} )[/tex] - log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x
Step-by-step explanation:
Given : Expression [tex]\log_2(9x^3)[/tex]
To find : Which expression is equivalent to given expression ?
Solution :
Expression [tex]\log_2(9x^3)[/tex]
Applying logarithmic property, [tex]\log_{a}( MN ) = \log_{a}( M) + \log_{a}( N )[/tex]
[tex]\log_{2}(9 {x}^{3} ) = \log_{2}(9 ) + \log_{2}( {x}^{3} )[/tex]
Using property, [tex]\log_{a}( { M}^{n} ) =n \log_{a}( { M})[/tex]
[tex]\log_{2}(9 {x}^{3} )=\log_{2}(9 ) +3 \log_{2}( {x} )[/tex]
i.e. log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x
Therefore, option 1 is correct.
