Expand log4(64)+log4( x5 )

Question

The answer key says 3+5log4x but I don't understand how to get that's the correct answer.

Answer 1

Recall that log_aa = 1 and log_a(b^r) = r(log_ab)

 

So, log₄64 + log₄(x⁵) = log₄(4³) + 5log₄x

 

                              = 3(log₄4) + 5log₄x = 3 + 5log₄x

Answer 2

log4*(64)+log4*(x⁵)=log(4⁴)+log4+log(x⁵)

                              =4*log4+log4+5*logx

                              =5*log4+5*logx

                              =5*(log4+logx)

                              =5*log(4*x)

This the right answer

 

I hope it will help

 

Regards,