Evaluating Log Expression

Question

I'm seeking some help. I've got this question to evaluate the log expression:

Log Expression

I realise I can get rid of the 2 and 3 by putting them on the exponent of both 1000 and 27. But that's as far as I've got. This is what I have so far:

https://i.stack.imgur.com/HClRB.jpg

What next steps should I take? Thanks for the help in advance.

Answer 1

$$\log_{10}1000$$ solves for $x$ in the following equation:

$$10^x=1000$$

Likewise the other two solve for $y$ and $z$ in:

$$3^y=27$$ $$4^z=64$$

You should be able to solve these.

Then your answer is $2x+3y-z$

Answer 2

Hint: Write $$2\log_{10}10^3+3\log_{3}3^3-\log_{4}4^3$$