How do you write as a single logarithm #1/2 Log _b3 +1/2 Log_bx - 3 Log_b Z#?

1 Answer
Mar 15, 2018

Answer:

#log_b(sqrt(3x)/Z^3)#

Explanation:

Since #xlogy=logy^x#, we can write:

#log_bsqrt(3)+log_bsqrt(x)-log_bZ^3#

Since #loga+logb=log(ab)#, we write:

#log_bsqrt(3x)-log_bZ^3#

Since #loga-logb=log(a/b)#, we can write:

#log_b(sqrt(3x)/Z^3)#