# Finding x and y from two given logarithmic equations

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 $x,y$