## 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.

#### Percents, How do I figure out what is 20% of 100?

How do I figure out what is 20% of 100?

#### Write phrase as an algebraic expressio, carly spends \$5 for n notebooks.w

carly spends \$5 for n notebooks.w

#### Writing Equivalent Ratios, John can drive his car 15 miles on 2 gallons. Ho...

John can drive his car 15 miles on 2 gallons. How many gallons of gas will john need to drive 195 miles?

#### I need help, Do you accept screen shot because it is a graph.

Do you accept screen shot because it is a graph.

#### Quiz #5., Working together Jack and Bob can clean a place in 30 minutes. On...

Working together Jack and Bob can clean a place in 30 minutes. On his own, Jack can clean this place in 50 minutes. How long does it take Bob to clean the same place on his own?

5/4:3/7

#### Permutations, Subject identification numbers in a certain scientific resear...

Subject identification numbers in a certain scientific research project consist of three digits followed by three letters and then three more digits. Assume repetitions are not all

#### Slopes, why is the slope of two perpendicular line a negative reciprocal

why is the slope of two perpendicular line a negative reciprocal

7 ?(2+N)2 N=0

#### Basic fact, What is a Math Basic Fact?

What is a Math Basic Fact?  