Logarithmic equations are often used in various scales of measurement; reducing wide-ranging quantities to smaller scopes. Examples of logarithmic equations applications in real life are with earthquakes scale (Richter), sound scale (decibel), pH levels, radioactive decay, bacterial growth, population growth, continuous interest and more. Logarithmic equations are pretty useful; you might as well learn how to solve them.
To solve logarithmic equations you should first manipulate the equation to have log with the same base on both sides so you can drop the logs (the only way two logs can be equal if their arguments are equal). The next step is solving a linear or polynomial equation (we know how to do that), last but not least you should check the solutions by plugging them into the original equation (we can only plug positive numbers into a logarithm).
It’s easier than it sounds; let’s start with an example (click here):
Parallel lines have the same slope, to find the parallel line at a given point you should simply calculate the slope, calculate the y intercept, and you’re pretty much done.
Finding the equation of the perpendicular line is somewhat similar, only calculating the slope is trickier. The slope of the perpendicular line is the negative reciprocal of the line slope, in other words, when multiplying the slopes of two perpendicular lines you should get -1.
Here’s how to find the equation of the line that is parallel to a given line and passes through a given point (click here):
In short, type in Parallel, the line and the point:
Here’s how to find the equation of the line that is perpendicular to a given line and passes through a given point (click here):
A biquadratic equation is a quadratic function of a square, having the form f(x)= ax^4+ bx^2 + c. To solve you simply have to rewrite the equation as a quadratic equation: substitute x^4 with u^2 and x^2 with u, to get au^2+ bu + c. See previous post on solving quadratic functions here.
Don’t forget to substitute back and solve for x. You should get up to 4 solutions; it is a quartic equation after all.