log square root of 100 + 3log cube root of 100

Question

Evaluate the expression:

A) 1/3  B) 3/10   C)5  D)3

 

Answer 1

no base is given so assume 10 is the base

log(10)(100)^[1/2]+3log(10)(100)^[1/3]

log(10)(10)+3log(10)(10^[2])^([1/3]

1+3log10)(10)^[2/3]

1+(2/3)3log(10)(10)

1+2log(10)(10)

1+2=3    (log(10)(10)=1)

D) is the answer

Answer 2

log(sqrt(100)) = log10^1/2 = 1/2 log(100) = 1/2 * 2 = 1 

 

3*log(cuberoot(100)) = 3*log100^1/3 = 1/3 * 3log100 = 2

 

Ans = 1 + 2 = 3