How do you write the logarithmic expression as the sum, difference, or multiple of logarithms and simplify as much as possible for #log_4(sqrt x / 16)#?

1 Answer
Jul 5, 2015

Answer:

#log_4(sqrtx/16)= 1/2log_4(x) – 2#

Explanation:

Property: #log_b(x/y) = log_b x – log_b y#

So

#log_4(sqrtx/16)= log_4(sqrtx) – log_4(16)#

#log_4(sqrtx/16)= log_4(x^(1/2)) – log_4(4^2)#

Property: #log_b(x^d) =dlog_b x#

So

#log_4(sqrtx/16)= 1/2log_4(x) – 2log_4 4#

#log_4(sqrtx/16)= 1/2log_4(x) – 2×1#

#log_4(sqrtx/16)= 1/2log_4(x) – 2#