Question

Which expression is equivalent to [log9+1/2logx+log(x^3+4)]-log6

Answer 1

A.) log 3 sqrt x(x^3+4)/2

Answer 2

You probably looking to write the given expression as a single logarithm.

Remember the follwing rules:

log(ab)= log(a) + log(b)
log(a/b)=log(a) - log(b)
log(a)^b = b log(a)

Based on these rules, we can write the above expression as a single logarithm, as shown below:


`log(9)+ (1)/(2)log(x)+log( x^(3)+4)-log(6) \\ \\ =log(9)+ log(x)^{ (1)/(2) } +log( x^(3)+4)-log(6) \\ \\ =log( (9 √(x)( x^(3)+4) )/(6) ) \\ \\ =log( (3 √(x)( x^(3)+4) )/(2) )`