Question

Value of log1/3 to the base 9

Answer 1

Answer:

-1/2

Step-by-step explanation:

The answer is -1/2.

I have explained in the photo.

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Answer 2

Answer:

log₉ $\frac{1}{3}$ =  - $\frac{1}{2}$

Step-by-step explanation:

To find,

log₉ $\frac{1}{3}$

Solution:

Recall the formula

1. logₐ $\frac{M}{N}$ = logₐ M - logₐ N

2. logₐ 1 = 0

3. logₐ a= 0

4. $log_{a^n} (a^m) = \frac{m}{n}$

By applying the logarithm rule, logₐ $\frac{M}{N}$ = logₐ M - logₐ N we get

log₉ $\frac{1}{3}$ = log₉ 1 - log₉ 3

Since logₐ 1 = 0, we have

log₉ $\frac{1}{3}$ = 0 - log₉ 3

=  - (log₉ 3)

= -( $log_{3^{2}}3$)

By applying the logarithm rule $log_{a^n} (a^m) = \frac{m}{n}$, we get

=  - $\frac{1}{2}$  log₃ 3

Since logₐa = 1,

= - $\frac{1}{2}$

∴ log₉ $\frac{1}{3}$ =  - $\frac{1}{2}$

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