Question

Find the value of log 3 base 81.
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Answer 1

`log_(81) 3 = (1)/(4)`

Explanation:

`Let \; log_(81) 3 = x \\\therefore 3 = {81}^x ..(by\: changing\: in \: exponential\: form)\\\therefore 3^1 = {3}^(4x)\\\therefore 1 = 4x.\\(\because bases \: are \: equal,\: hence \: exponents\: will\: also\: be \: equal)\\\therefore x = (1)/(4)\\\\\huge\purple{\boxed{\therefore log_(81) 3 = (1)/(4)}}`

Answer 2

Exact value

Decimal form

0.47712125