Solve out the equations using simpler method, Algebra

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.

Posted Date: 4/8/2013 3:27:45 AM | Location : United States







Related Discussions:- Solve out the equations using simpler method, Assignment Help, Ask Question on Solve out the equations using simpler method, Get Answer, Expert's Help, Solve out the equations using simpler method Discussions

Write discussion on Solve out the equations using simpler method
Your posts are moderated
Related Questions
what is the answer to y is greater than 3x-l and y is less than x+2

There is interesting relationship among the graph of function and its inverse. Here is the graph of the function & inverse from the first examples. We'll not deal along with the

In the last two sections of this chapter we desire to discuss solving equations & inequalities that have absolute values.  We will look at equations along with absolute value in th


BEST WAY TO FIND ORDERED PAIRS

Show that x+3 is a factor of f(x)=3x4 - 3x3 - 36x2. Then factor f(x) completely.



The difference of two numbers is 18. The larger number is four more than twice the smaller. What are the numbers?

a stack of disks is 0.5cm thick.how many disk each at 0.125cm thick are in a stack?