Question

How to change base of logarithms: Best answer gets 27 points and brainliest answer

Answer 1

Answer:

1/3

Step-by-step explanation:

 To change from one base to another, we use the formula

Logb x = Loga x/Loga b

log1/9  (3^(1/3) /3)

log3 ((3^(1/3) /3))

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log3 (1/9)

Log a /b = log a - log b

and 1/9 = 3^-2

log3 ((3^(1/3) ) - log3 (3)

-------------------------

log3 (3^-2)

log a^b  = blog a

1/3 log3 (3 ) - log3 (3)

-------------------------

-2log3 (3)

We know log3 (3) =1

1/3 (1) - 1

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-2 (1)

1/3  - 1

-------------------------

-2

-2/3

------

-2

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-2/3 * -1/2

1/3