# LOG Excel Formula

Exponential and log functions are essential mathematical function with broad applications, which includes studies related to the population growth, compound interest and radioactive decay. The exponential function has form:

**F (x) = C* b^x**

**Where,**

- B is the positive invariable known as base
- C is the arbitrary constant normally positive
- X plays and essential role as exponent

If b is larger than one, then f (X) augment with x, or else it decrease with x, even a comparatively small base results in speedy growth. One sample of the exponential function is the compound interest rates compounded yearly would grow as per the formula:

**A (t) = 1000 * (1.05) ^t,**

Where, T is number of year that the money has been invested; such investment will be doubled in each fourteen years.

An additional example of roughly exponential population growth is as under. The region with fixed population growth rates has population that grows in accordance to formula, which is:

**P (t) = PO * (1+r) ^t,**

Where, PO is an initial population; P (t) is population after t years; r is annual population growth rates.

In February last 2008, the population of the world has been estimated to be 6.65 billion with yearly growth rates of 1.17 percent. At that time, the population of the world would reach around 10.85 billion by year 2050.

Another vital example of exponential functions is the radioactive crumble. The quantity of the radioactive essence with half life of T- ½ decays in accordance to formula which is:

**N (t) = N (0)* 2’ (-t/T_1/2)**

The radioactive isotopes are being used to identify the age fossils as ancient artifact with that formula.

**Domain and Range of Logarithmic Function**

Let f(x) = logX

Since exponential function is an inverse of logarithmic function, the range of logarithmic function is domain of exponential function which is set of real numbers.

The domain of logarithmic function is a range of exponential function which is provided by interval (0 + infinity).

**Interactive Tutorials:**

1 – Use sliders on left side of control panel of applet to the set of a=1; b =1; then c = 0; d = 0, and then change B. examine the domain and the range of log function.

**Shifting, Reflection, and Scaling of Graph of Log Functions:**

- Investigate the base B, which include set a=1; b =1; then c = 0; d = 0 with the use of scroll bar. The set B to value between zero and one and to value more than one, remember of various graphs acquired and explained.

- Investigate the effect of parameter (vertical scaling) by setting the B = e, b=1, then c=0 and d=0

- Investigate the effect of parameter B the (horizontal scaling) by setting a=1; b =1; then c = 0; b=e.

- Set b= e, then a=1, and b=1 and study the effect of C (the horizontal shifting) and then D (vertical translation).

- Set b and to a few values and then explain how parameter b and c affects the domain of log function. Explain this analytically.

- What parameters affect the x intercept? Are there x intercept?

- What parameters affect the y intercept?

These are the questions that you can have to study the function.

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