REFLECTION OF MATH

This video is dealing with logarithms. the first rule that you should remember is about log b of x equals y. basically, b is called the base and then u can rewrite in other formula that is b y equals x.

Logarithm sometimes does not make senses but i gonna make it sense with making some notations.

The notations is that if you have a log base ten of x, u can only write it with log x. it's just th same. likewise with log base 'e' (some irrational number, just like phi) of x, we can only write it with lnx (l n of x) or we can say it with natural logarithm. so natural logarithm is just thesame with lnx.

So, we have a couple problem here and we will finish this using the first property with the expanantial form. if we want to evaluate log base ten of one hundred equals x, we have to notice the first pattern, the base raises to the power so b raises to the y equals x. so we have the same pattern for this problem (log 10 of 100=x), ten raises to the x equals 100. so dont say x equals 100 because x is the exponent, so u should say ten squared equals 100 that means x value is 2. so all that means is that log base ten of one hundred is equals the number of two.

The same way in the problem log base two of x equals 3 , and we will find the value of x. so u should invert the form becomes two third power equals x meaning 8 equals x. and finally we can find that log of two of eight equals three.

Move the next example, suppose we have log of seven of one over forty nine is some number called x. so i will rewrite it using exponent. so we can write 7 raises to the x power being equals to one over fortinine. seven squared is 49 but we dont need that, we need one over 49 so it becomes one over seven square.

And we can find seven power of x equals seven power of minus two because we should change the sign of the exponent.

And finally find the power should be equals meaning that x equals to negatif two.

Now move to the some properties u should know, suppose we have log base b of m times n with the rule log base b of M plus log base b of N because product (perkalian) turns into addition.

The next one says that log b of M divided by N so it becomes log base b of M minus log base b of N.

And the last but not least is about exponent rule, suppose u have log base b of x raises to the n power, it becomes n times log base b of x.

We have an example here.

We have log base 3 of squared times y plus one over z cubed. so use the middle property, it is the division property.

So it becomes log base 3 of x squared times y plus one minus log base 3 of z cubed. and the next step is to brake up the first part into addition and we will have log base 3 of x squared plus log base 3 of y plus one minus log base 3 of z cubed.

And the last step is we will use the exponent rule, so we have 2 times log base 3 of x plus log base 3 of y plus one minus 3 times log base 3 of z.

So those are the expanssion of the properties.