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I'm just studying some further mathematics units for my own benefit before I undertake a PHD in chemical engineering next year. I feel the learning of the mathematical concepts at this level will help me massively as I seek to take a leap into the next stage of academia. I've been doing well all week, specifically looking at how the rules of logarithms apply, what they are and how to figure out a multitude of things relating to logs in mathematical scenarios.

I've found this question towards the back of one of the textbooks:

Given that $ \log_2(x - 5y + 4) = 0 \ $ and $ \ \log_2(x + 1) -1 \ = \ 2 \ \ \log_2 y \ $, find x and y.

I've been staring at my log rules for the past 20 minutes and I have several versions of how I could rearrange these equations for further derivations. What would be the most useful first step to take however? To multiply out, logs all in?

Thanks for any assistance.

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The log of $1$ is zero in any base, so the first gives you $x-5y+4=1$. Raise $2$ to the power of both sides of the second equation, remembering that $2^{\log_2 z}=z$. Using the laws of exponents, the second will give you a second linear equation in $x,y$

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  • $\begingroup$ I'm lost at the point that the 2 is involved in the second. How is this part established? $\endgroup$ – New Zealand's finest May 5 '16 at 4:47
  • $\begingroup$ It is the base of the logarithms that are in the equation. $\endgroup$ – Ross Millikan May 5 '16 at 5:29
  • $\begingroup$ Okay so I'm headed for a second linear equation y is for sure $\endgroup$ – New Zealand's finest May 5 '16 at 10:39

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