Evaluate [log(5)+log(2)]/log₂(∛10) using logarithm laws

[lucky_star]

Hi, I have a log problem. Can anyone please check if I did it correctly!?

Homework Statement

Evaluate the following using the laws of logarithms.
Simplify your answer as much as possible. (Note:
These should be done without a calculator).

[log(5)+log(2)] / log₂(cubic root of 10)
= log(5*2) / log₂ (10)^1/3
= log(10) / 1/3*log₂(10)
= 3 / log₂(10)


Is this simplified correctly? Can we simplify more?

 

[symbolipoint]

Good.

 

[lucky_star]

Thank you!

 

[symbolipoint]

Know this: Your notation is faulty near the end of your steps.

This, "= log(10) / 1/3*log2(10)" is not what you meant.
You really meant and should have written, log₂(10)/(1/3)*log₂(10)

 

[HallsofIvy]

That is because 1/ab is normally read as 1/(ab), not as (1/a) b.

 

[lucky_star]

Yes, that what I meant symbolipoint. Thank you everybody! I need to pay more attention on how I write it properly.