write $\log_42x$ in the form $y =\log_4x+k$

Question

write $\log_42x$ in the form $y = \log_4x+k$

I take it this is one of the log rules but I don't see which and I do not understand where k comes from or what the constant stands for.

Answer 1

Use formula: $\log_c ab= \log_c a+ \log_c b:$ $$\log_4 2x=\log_4 2+\log_4 x= \frac12+\log_4 x$$