solve 4loga(x)=loga(81)?

4 logₐ(x) = logₐ(81)
logₐ(x⁴) = logₐ(81)
x⁴ = 81
x = 3  or  x = -3 (rejected for logₐ(-3) is indefined.)
Hence, x = 3

4log(base a)x = log(base a)81
log(base a)(x^4) = log(base a)81
x^4 = 81
x = 3

Remember 81 - 3^4 
Hence 
4log(a)X = log(a)3^4 
4log(a)X = 4log(a)3 
Cancel down by '4' 
log(a)X= log(a) 3 
Antilog 
X = 3 

4loga(x) = loga(81);
ie., loga(x^4) = loga(81);
Therefore x^4 = 81;
ie., x = 3;

4 log a (x) = log a (81)
x^4 = 81
Solution:
x = 3