Question

log
$9 \sqrt{3}$
to to the base 1/3 is

Answer 1

Hi ,

9√3 = 3² × 3^1/2

= 3 ^( 2 + 1/2 )

= 3^5/2 ----( 1 )

1/3 = 3^-1 ----------( 2 )

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log a^m base a^n = m/n

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log 9√3 base 1/3

= log 3^5/2 base 3^-1

= ( 5/2 ) / ( - 1 )

= - 5/2

I hope this helps you.

:)

Answer 2

Given log 9 root 3 to the base 1/3.

It can be written as log 1/3(9 root 3).

We know that log to the base 1/a(x) = -loga(x).

log 1/3(9 root 3) = - log3 (9 root 3).

We know that log(ab) = log a + log b.

 -log3(root 3) + log(9).

= -log3(root 3) + log3(3^2)

= -log3(root 3) + log3(2 log 3)

= -log3(root 3 + 2 * 1)

= -log3(root 3 + 2)

= -log3(3^1/2 + 2)

= -1/2 log3(3) + 2

= -( 1/2 * 1 + 2)

= -5/2.


Therefore log 9 root 3 to the base 1/3 = -5/2.

Hope this helps!