college algebra

Question

write the equation in its equivalent logarithmic form

 

³square root 125=5

Answer 1

So I think the original would look like this ->    ³√125=5

 

This is read aloud as the cube root of one hundred twenty five is 5.

 

A cube root is equivalent to an exponent of 1/3, so we can rewrite the above as

 

125^1/3=5

 

Since the log keeps the same base and reverses the process of an exponent, this leaves us with

 

Log₁₂₅(5)=1/3

 

That is probably all they are asking for. You could also use a change of base since Log₁₂₅(x) is not a function on most calculators, but all that was asked for was the equivalent logarithmic expression, so I would stop there.

Answer 2

³√125 = 5

 

(125)^1/3 = 5

 

log₁₂₅(5) = 1/3