Evaluating Log Expression

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.imgur.com/NG7ekNk.jpg?2

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

• Welcome to MSE. Please type your questions where practicable, as in this case, instead of posting images. Images can't be browsed. – saulspatz Nov 3 '18 at 15:43
• @saulspatz Oh alright, thanks for letting me know. Will make it it doesn't happen again. – Diamonds Nov 3 '18 at 16:07

$$\log_{10}1000$$ 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 $$2x+3y-z$$

• Alright, I see thanks for your help Dr Sonnhard and thanks to Rhys I've been able to get my answer to be 12. Much appreciated. I can't give you guys an upvote as I don't have the required reputation. – Diamonds Nov 3 '18 at 15:51

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

• Alright, I see thanks for your help Dr Sonnhard and thanks to Rhys I've been able to get my answer to be 12. Much appreciated. – Diamonds Nov 3 '18 at 15:51
• Also, thanks for this. I will keep this in mind next time. 6+9-3 = 12. Thanks for the hint @Dr. Sonnhard Graubner – Diamonds Nov 3 '18 at 16:11