Question

Find the value of log 3 base 81.​

Answer 1

Answer:

$log_{81} 3 = \frac{1}{4}$

Step-by-step explanation:

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

Answer 2

Exact value

Decimal form

0.47712125