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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.

Diamonds
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    Welcome to MSE. Please type your questions where practicable, as in this case, instead of posting images. Images can't be browsed. – saulspatz Nov 03 '18 at 15:43
  • @saulspatz Oh alright, thanks for letting me know. Will make it it doesn't happen again. – Diamonds Nov 03 '18 at 16:07

2 Answers2

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

Dr. Sonnhard Graubner
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  • 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 03 '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 03 '18 at 16:11
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$$\log_{10}1000$$ 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 $2x+3y-z$

Rhys Hughes
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  • 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 03 '18 at 15:51