Solve out the equations using simpler method, Algebra

Assignment Help:

Example   Solve out each of the following equations.

                             7x = 9

Solution

Okay, although we say above that if we contained a logarithm in front the left side we could obtain the x out of the exponent. That's simple enough to do. We'll only put a logarithm in front of the left side. But, if we put a logarithm there we also have to put a logarithm in front of the right side. Commonly this is referred to as taking the logarithm of both sides.

We can employ any logarithm that we'd like to thus let's try the natural logarithm.

ln 7x  = ln 9

x ln 7 = ln 9

Now, we have to solve for x. it is easier than it looks.  If we had 7 x = 9 then we could all solve out for x simply by dividing both of the sides by 7.  It works in accurately the same manner here.  Both ln7 & ln9 are only numbers. Admittedly, it would take a calculator to find out just what those numbers are, however they are numbers & so we can do the similar thing here.

x ln 7/ ln 7 = ln 9/ ln 7

x = ln 9/ ln 7

Now, technically i.e. the exact answer.  Though, in this case usually it's best to get a decimal answer so let's go one step further.

x = ln 9 / ln 7= 2.19722458 /1.94591015= 1.12915007        

Note down that the answers to these are decimal answers more frequently than not.

Also, be careful to not make the following mistake here.

1.12915007 = ln 9/ ln 7 ≠ ln ( 9 /7)=0.2513144283

The two are apparently different numbers.

At last, let's also utilizes the common logarithm to ensure that we get the same answer.

log 7x  = log 9

x log 7 =log 9

x =log 9/ log 7 = 0.954242509 /0.845098040= 1.12915007 

Thus, sure enough the similar answer. We can use either logarithm, even though there are times while it is more convenient to employ one over the other.


Related Discussions:- Solve out the equations using simpler method

Polynomials, please help me understand polynomials- i get the small problem...

please help me understand polynomials- i get the small problems but i dont understand larger ones

Factoring, How can x raised to the second power mines x mines 2 . can be fa...

How can x raised to the second power mines x mines 2 . can be factored as (x+1)(x-2)

Word problems, can you help me solve this problem?

can you help me solve this problem?

Quarditic, what is quarditic equation

what is quarditic equation

Math, 4(3x-2) -5(x+1)=6-(4x-3)

4(3x-2) -5(x+1)=6-(4x-3)

Equations with more than one variable, Here we'll be doing is solving equat...

Here we'll be doing is solving equations which have more than one variable in them.  The procedure that we'll be going through here is very alike to solving linear equations that i

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd