Question

the vakue of log 1/3 to the base 9 is​

Answer 1

Answer:

$\large\boxed{\sf{-\dfrac{1}{2}}}$

Step-by-step explanation:

We have to find the value of,

$log_{9}( \frac{1}{3} )$

After simplifying, we get

$= log_{ {3}^{2} }( {3}^{ - 1} ) \\ \\ = - \frac{1}{2} log_{3}(3) \\ \\ = - \frac{1}{2} \times 1 \\ \\ = - \frac{1}{2}$

Concept Map:-

• $log_{a}(a) = 1$

• $log_{ {x}^{b} }( {y}^{a} ) = \frac{a}{b} log_{x}(y)$

Answer 2

Answer:

Log₉(1/3) = -1/2

Step-by-step explanation:

Log₉(1/3) can be expressed in the form of (logₓy = logₐy / logₐx)

we can write it as

Log₉(1/3) = -log₁₀(3) / log₁₀(3²)

here we used  [logₓ(1/y) = -logₓy)]

Log₉(1/3) = -log₁₀(3) / 2log₁₀(3)

Log₉(1/3) = -1/2