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PLEASE HELP ASAP!!!!

PLEASE HELP ASAP class=

Sagot :

Answer:

2

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

let

[tex]log_{2}[/tex] 8 = n ⇒ 8 = [tex]2^{n}[/tex] , that is

2³ = [tex]2^{n}[/tex] ( equate exponents )

n = 3

and let

[tex]log_{3}[/tex] ( [tex]\frac{1}{3}[/tex] ) = n ⇒ [tex]\frac{1}{3}[/tex] = [tex]3^{n}[/tex] , that is

[tex]3^{-1}[/tex] = [tex]3^{n}[/tex] ( equate exponents )

n = - 1

then

[tex]log_{2}[/tex] 8 + [tex]log_{3}[/tex] ([tex]\frac{1}{3}[/tex] )

= 3 + (- 1)

= 3 - 1

= 2

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