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Use the laws of logarithms and the values given below to evaluate the logarithmic expression (picture provided)

Use the laws of logarithms and the values given below to evaluate the logarithmic expression picture provided class=

Respuesta :

carlosego

Answer: option b.

Step-by-step explanation:

To solve the given exercise, you must keep on mind the following law of logaritms:

[tex]m*log(a)=log(a)^m[/tex]

Descompose 8 into its prime factors:

[tex]8=2*2*2=2^3[/tex]

Therefore,  you can rewrite the expression given, as following:

[tex]log8=log2^3=3log2[/tex]

You know that [tex]log2=0.3010[/tex]

Then, when you substitute, you obtain:

[tex]3*0.3010[/tex]≈0.9030

Wolfyy

Factor out 8 using 2.

log(8) = log(2^3)

Use the product rule [ log(xy) = log(x) + log(y) ] to simplify.

log(2^3) = 3 log(2)

Simplify using the given value for 2.

3(0.3010)

0.9030

Therefore, log(8) ≈ 0.9030 (Option B)

Best of Luck!

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