Given the expression [tex]b^{3c+1}=5a-d.[/tex]
Take a logarithm [tex]\log_b[/tex] from both side of the given expression:
[tex]\log_b b^{3c+1}=\log_b (5a-d).[/tex]
From the property [tex]\log_a a^x=x,[/tex] you have that
[tex]\log_b b^{3c+1}=3c+1.[/tex]
Then
[tex]3c+1=\log_b (5a-d).[/tex]
Answer: correct choice is C
