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Simple Tips for Better Maths Results!

logarithm equations

Linear Law,Just 1 Strategy Makes A Grade Difference

What is Linear Law?

It is a tool which will allow you to transform non-straight line equation to straight line equation so that you can plot a straight line. Most of the time, the axis will consist of x and/or y

One of the techniques involving taking lg (log base 10) on both sides of the given equation.

linearlawquestion1.PNG

Common Mistake! STOP
y=Ax^b=>lgy=blgAx=>blgA+blgx

This is one of the common mistakes I have highlighted in Top 7 Commonly Made Mistakes in Logarithm

How To Counter This Mistake

Very simple. Just add in a bracket on the right hand side of the equation.
y=(Ax^b)<br> =>lgy=lg(Ax^b)<br> => lgy=lgA+lgx^b<br> => lgy=lgA+blgx<br>

Now, your y-axis will be lg y and x-axis will be lg x. Gradient = b and y-intercept = lg A

Logarithm Equation Question 3

This is an interesting question which I came across under Additional Mathematics (A-Math):

Find the value of x.

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

Who is courageous to work on this question?

I will respond to this question when someone discusses about this question first :)

Update:

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(Apply Power Law)

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(multiply by 4 on both sides of equal sign)

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(Apply Power Law)
(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(Apply Quotient Law)
(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}
(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(Factorise)

(log_x \sqrt{3})(log_x\sqrt{8})= \frac{3}{2}log_x\frac{1}{\sqrt{2}}

(log_x8)=0 (NA)or log_x3+1=0

log_x3=-1,3=x^-^1,3=\frac {1}{x},3x=1,x= \frac {1}{3}

Top 7 Commonly Made Mistakes in Logarithm

How many of you would like to learn Math faster?
And how many of you would like to score more marks for Math?

Do you know that one of the fastest and effective techniques to grasp something fast would be to learn the mistakes that many others are commonly making and thus avoid them at all cost!

I am going to share with you the Top 7 Commonly Made Mistakes in Logarithm.

Please note all these are mistakes so do not follow instead you must be aware of them and constantly remind yourself not to fall into the same trap.

(Click on it to have a better view)


logmistakes-big.PNG
(Click on it to have a better view)

Hundreds of students receive a link to this file via their email so that they can save the the file and print it out for reference. If you want to be like them, be sure to subscribe to my mailing list. Click here >>

Logarithm Equation Question 1

I met a student and she passed me this paper with this Lg question on it, asking me on the solution for solving this equation :\lg(x-2)=(lg3)^2

Coincidentally, I was asking a few O Level students of mine on which are the "Killer A-Maths Topics" for them. Logarithm, Indices, Surds is one of the common topic which is ranked high on their list.

Now back to the question.

PS:lg = log_{10}

Notice that right hand side of the equal sign is something you can compute using the calculator hence,

\lg(x-2)=(lg3)^2
(x-2)= 10^{(lg3)^2}

Use your calculator to find out the value of 10^{(lg3)^2} and the value is 1.69 ( round off to 3 significant figure) so the answer for this question is

x = 1.69 + 2<br> =3.69<br>

I will be coming out with a series of posts on Logarithms since it is a "hot" topic for students :-) Subscribe to my feeds to be updated of this post.