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Evaluate the following expression using the properties of logarithms.

log subscript 4 left parenthesis 4 right parenthesis plus log subscript 4 left parenthesis 16 right parenthesis plus log subscript 4 left parenthesis 64 right parenthesis


10


9


6


17



Answer :

eyshbakar

Answer:

Step-by-step explanation:

The properties of logarithms that we can use to evaluate this expression are the logarithm of a power and the logarithm of a product.

log subscript 4 left parenthesis 4 right parenthesis = log subscript 4 left parenthesis 2^2 right parenthesis = 2 * log subscript 4 left parenthesis 2 right parenthesis = 2

log subscript 4 left parenthesis 16 right parenthesis = log subscript 4 left parenthesis 2^4 right parenthesis = 4 * log subscript 4 left parenthesis 2 right parenthesis = 4

log subscript 4 left parenthesis 64 right parenthesis = log subscript 4 left parenthesis 2^6 right parenthesis = 6 * log subscript 4 left parenthesis 2 right parenthesis = 6

Therefore, the expression simplifies to:

log subscript 4 left parenthesis 4 right parenthesis + log subscript 4 left parenthesis 16 right parenthesis + log subscript 4 left parenthesis 64 right parenthesis = 2 + 4 + 6 = 12

The answer is 12.

semsee45

Answer:

6

Step-by-step explanation:

Given logarithmic expression:

[tex]\log_{4}\left(4\right)+\log_{4}\left(16\right)+\log_{4}\left(64\right)[/tex]

Rewrite 16 as 4² and 64 as 4³:

[tex]\implies \log_{4}\left(4\right)+\log_{4}\left(4\right)^2+\log_{4}\left(4\right)^3[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies \log_{4}\left(4\right)+2\log_{4}\left(4\right)+3\log_{4}\left(4\right)[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies 1+2(1)+3(1)[/tex]

Simplify:

[tex]\implies 1+2+3[/tex]

[tex]\implies 3 + 3[/tex]

[tex]\implies 6[/tex]

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