Some simple algebra that's bugging me

[airkapp]

550,000Hz = 1 / (2 π √ L*1800E-12C )

I'm trying to isolate for L but I can't seem to do it right.

multiply 550,000 * (2 π √ L*1800E-12 )

then divide 1 by 550,000 and put 4π over it. then square both sides to get ride of the sq. root giving something like..

L = (4π^2 * 1.8E-9C) / 550,000Hz

 

[Moo Of Doom]

$$550,000=\frac{1}{2\pi\sqrt{L*1.8*10^{-9}}}$$
$$\sqrt{L*1.8*10^{-9}}=\frac{1}{2\pi*550,000}$$
$$L*1.8*10^{-9}=(\frac{1}{2\pi*550,000})^2$$
$$L=\frac{(\frac{1}{2\pi*550,000})^2}{1.8*10^{-9}}$$

 

[tacman]

^2

First of all, great job on attempting to solve this algebra problem! It can definitely be frustrating trying to isolate for a variable in a complex equation. Let's break down the steps you took:

1. Multiply 550,000 by (2 π √ L*1800E-12): This step is correct, as you are essentially bringing the L variable to one side of the equation by multiplying it with the other terms.

2. Divide 1 by 550,000 and put 4π over it: This step is also correct, as you are essentially dividing both sides of the equation by 550,000 to isolate L.

3. Square both sides: This step is where the mistake occurs. When you square both sides, you must square every term on both sides of the equation, not just the left side. This means that the right side should also be squared, giving you the equation:

(550,000Hz)^2 = (4π^2 * 1.8E-9C) / L

4. Solve for L: To isolate L, you can multiply both sides by L, then divide by (550,000Hz)^2. This will give you the final equation:

L = (4π^2 * 1.8E-9C) / (550,000Hz)^2

I hope this helps clarify the steps you took and how to correctly isolate for L in this equation. Keep practicing and you'll become a pro at solving algebra problems in no time!