Verified Answer :

kudzordzifrancis

ANSWER

\(log_{b}( {a}^{d} ) = d \: log_{b}(a)\)

EXPLANATION

This is a straightforward property of logarithm.

It was derived from one of the laws of indices as follows,

Let
\(a= {b}^{m} - - (1)\)

We can write this as a logarithmic equation to get,

\(m = log_{b}( a ) - - (2)\)

When we raise both sides of equation (1) to the exponent of d, we get

\({a}^{d} = ( {b}^{m} )^{d}\)

\({a}^{d} = ( {b}^{md} )\)

We rewrite this last equation as logarithm

\(log_{b}( {a}^{d} ) =md\)

\(m = log_{b}( a )\)

This implies that
\(log_{b}( {a}^{d} ) = d log_{b}( a )\)

The correct answer is C

animaljamarctic

Answer: The multiplication one

C. d · log(b) a

Hope this helps :)

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