Log of letters

Question

Given that a=c³ and b=√c ,  evaluate log_ab

 

Answer 1

log_ab  can be read as a raised to some number is b.

 

 

c³ raised to what number (x) is c^1/2.

 

 

(c³)^x = c^1/2

 

Since the bases are the same, we just equate the exponents.

 

3x = 1/2

 

Solving for x, we get

 

x = 1/6

 

 

Therefore,  log_ab = 1/6