Answer :
ANSWER
[tex] log_{b}( {a}^{d} ) = d \: log_{b}(a) [/tex]
EXPLANATION
This is a straightforward property of logarithm.
It was derived from one of the laws of indices as follows,
Let
[tex]a= {b}^{m} - - (1)[/tex]
We can write this as a logarithmic equation to get,
[tex]m = log_{b}( a ) - - (2)[/tex]
When we raise both sides of equation (1) to the exponent of d, we get
[tex] {a}^{d} = ( {b}^{m} )^{d} [/tex]
[tex] {a}^{d} = ( {b}^{md} )[/tex]
We rewrite this last equation as logarithm
[tex] log_{b}( {a}^{d} ) =md[/tex]
[tex]m = log_{b}( a ) [/tex]
This implies that
[tex] log_{b}( {a}^{d} ) = d log_{b}( a ) [/tex]
The correct answer is C
[tex] log_{b}( {a}^{d} ) = d \: log_{b}(a) [/tex]
EXPLANATION
This is a straightforward property of logarithm.
It was derived from one of the laws of indices as follows,
Let
[tex]a= {b}^{m} - - (1)[/tex]
We can write this as a logarithmic equation to get,
[tex]m = log_{b}( a ) - - (2)[/tex]
When we raise both sides of equation (1) to the exponent of d, we get
[tex] {a}^{d} = ( {b}^{m} )^{d} [/tex]
[tex] {a}^{d} = ( {b}^{md} )[/tex]
We rewrite this last equation as logarithm
[tex] log_{b}( {a}^{d} ) =md[/tex]
[tex]m = log_{b}( a ) [/tex]
This implies that
[tex] log_{b}( {a}^{d} ) = d log_{b}( a ) [/tex]
The correct answer is C
Answer: The multiplication one
C. d · log(b) a
Hope this helps :)