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.


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 $x,y$

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.