Algebra 2: How to Solve Log Equations

Welcome to Mathsux! Today, we’re going to go over how to solve logarithmic equations, yay! But before we get into finding x, though, we need to go over what logarithms are and why we use them in the first place…..just in case you were curious!

Also, if you have any questions about anything here, don’t hesitate to comment below or shoot me an email.  Happy calculating! 🙂

Logarithms are the inverses of exponential functions.  This means that when graphed, they are symmetrical along the line y=x.  Check it out below!

Screen Shot 2020-06-24 at 9.29.23 PM.png

When on the same set of axis, notice how the functions are symmetrical over the line y=x:

Screen Shot 2020-06-24 at 9.30.16 PM

We use logarithms to find the unknown values of exponents, such as the x value in the equation, Screen Shot 2020-06-24 at 9.30.55 PM.png.  This is a simple example, where we know the value of x is equal to 2,(Screen Shot 2020-06-24 at 9.32.30 PM.png). But what if it were to get more complicated?  That’s where logs come in!

Logarithms follow a swooping pattern that allows us to write it in exponential form, let’s take a look at some Examples below:Screen Shot 2020-06-24 at 9.34.16 PM.pngBut wait there’s more! Logs have a certain set of Rules that makes working with them easier! Check it out below:

Screen Shot 2020-06-24 at 9.35.10 PMWe can use these rules to help us algebraically solve logarithmic equations, let’s look at an example that applies the Product Rule.

Screen Shot 2020-06-24 at 9.36.08 PM.png

Screen Shot 2020-06-24 at 9.36.50 PM

Screen Shot 2020-06-24 at 9.46.07 PM.pngScreen Shot 2020-06-24 at 9.38.32 PM

Try the following practice questions on your own!

Practice Questions:

Screen Shot 2020-06-24 at 9.39.16 PM.png

 

 

 

 

 

 

Solutions:

Screen Shot 2020-06-24 at 9.40.37 PM

Still got questions?  No problem! Check out the video that goes over the same example outlined above.  And for more info. on logarithms check out this post that goes over a NYS Regent’s question here.  Happy calculating! 🙂

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****Check out this Bonus Video on How to Change Log Bases****

 

 

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