Question

find the value of log216base6root6 ​

Answer 1

Answer:

2

Step-by-step explanation:

216 can be expressed in the form of 6 × 6 × 6

which can be written as

$216 = 6 {}^{3}$

But it is not useful to us as base is 6√6

Therefore we can express 216 in the form

216 = 6 × 6 × 6 = 6 × 6 × √6 × √6

$216 = (6 \sqrt{6} ) {}^{2}$

Therefore By putting the value

The Expression Become

$log_{6 \sqrt{6} }((6 \sqrt{6}) {}^{2}$

Since we know that power comes in the multiply

it can be written as

$2 log_{6 \sqrt{6} }(6 \sqrt{6} )$

Since We know that function log having value and base same becomes 1

Hence 2×1 = 2

Therefore Final Answer is 2