Log5 (3+x^2)= log2 28

Question

Log5 (3+x^2)= log2 28

Answer 1

Log5 (3+x^2)= log2 (28)

Одз: 3+х²>0 ; х²> -3 (всегда)

log5 (3+x²)= log2 (7·4)
5^( log2 (7·4) )= 3+x²
5^( log2(4)+log2(7) )= 3+x²
5^( 2+log2(7) )= 3+x²
5²·5^log2(7) = 3+x²
5²·5^log2(7)–3 = x²

±( 5²·5^log2(7)–3 )^½ = x²