## Evaluate the logarithms, Algebra

Assignment Help:

Example   Evaluate following logarithms.

log4 16

Solution

Now, the reality is that directly evaluating logarithms can be a very complicated process, even for those who actually understand them.  Usually it is much convenient to first convert the logarithm form into exponential form.  In that form usually we can get the answer pretty quickly.

What we are actually asking here is the following.

log4 16 = ?

As recommended above, let's convert this to exponential form.

log4 16 = ?        ⇒ 4 ? = 16

Most of the people cannot evaluate the logarithm log4 16 right off the top of their head.  Though, most of the people can determine the exponent which we need on 4 to obtain 16 once we do the exponentiation.  So, since,

42  = 16

we need to have the following value of the logarithm.

log4 16 = 2

Expectantly, now you have an idea on how to evaluate logarithms & are beginning to get a grasp on the notation. There are a few more evaluations which we desire to do though, we have to introduce some special logarithms which occur on extremely regular basis. They are the common logarithm & the natural logarithm.  Following are the definitions & notations which we will be by using for these two logarithms.

common logarithm :    log x = log10 x

natural logarithm :       ln x =loge x

Thus, the common logarithm is just the log base 10, except we drop the "base 10" part of the notation.  Alike, the natural logarithm is just the log base e  along with a different notation and where e is the similar number which we illustrates in the earlier section and is defined to be

e = 2.718281827.

#### Symmetry, In this section we will take a look at something that we utilized...

In this section we will take a look at something that we utilized back while we where graphing parabolas.  Though, we're going to take a more common view of it this section. Severa

#### Equivalent values, two debts- the first of 800 is due six month ago and the...

two debts- the first of 800 is due six month ago and the second of 1400 borrowed one year ago for a term of three years at 6.5% compunded annulallu are to be replaced by a single p

#### Determine the relationship between the first and second numb, 6 is to 15 as...

6 is to 15 as 36 is to

#### Use the quadratic formula to solve equation, A college student invested par...

A college student invested part of a \$25,000 inheritance at 7% interest and the rest at 6%.  If his annual interest is \$1,670 how much did he invest at 6%?  If I told you the answe

#### How do I solve algebra word problems?, Bills Roast Beef sells 3 times as m...

Bills Roast Beef sells 3 times as many sandwiches as Pete''s deli. The difference between their sales is 170 sandwiches. How many sandwiches did each sell?

x-5/6

#### Present value of annuity, The Fritzes are buying a house that sells for \$18...

The Fritzes are buying a house that sells for \$185,000. The bank is requiring a minimum down payment of 15% for a 30-year mortgage at 5.2% interest. Find (a) the amount of the down

#### Find solution using quadratic equation, Two cars start out at the similar p...

Two cars start out at the similar point.  One car starts out moving north at 25 mph. later on two hours the second car starts moving east at 20 mph.  How long after the first car s

#### Finding relations for given solutions, The slope is -3 and the y-intercept ...

The slope is -3 and the y-intercept is 4. How do I find a relation in the form y=mx+b which has a solution set line satisfying the given conditions?

#### Inconsistent systems example, Inconsistent systems example Example Solv...

Inconsistent systems example Example Solve the given systems of equations. x - y = 6 -2x + 2 y = 1 Solution We can utilize either method here, although it looks l