What's the fastest way to find Anti Logarithms(not using interpolation or a log table)

can anyone give me an example using any kind of value? (preferably solving triangles)

I answered this for you in detail here, and you even responded with a "Thanks"

http://www.jiskha.com/display.cgi?id=1379417550

Why are you asking the same question again ?

For small arguments, you can use the series expansion of the exponential function. For large arguments, you can subtract a multiple of log(2)to make the argument smaller and then use the series expansion on that smaller argument.

E.g.:

exp(7) = 2^10 exp[7 - 10*log(2)] =

2^10 exp(0.0685281944)

To find the antilogarithm without using interpolation or a log table, you can use the exponential function. The antilogarithm of a number is the inverse operation of logarithm.

Here is an example of finding the antilogarithm of a number to solve a triangle:

Suppose you have a right triangle with one angle given and the lengths of two sides. To find the length of the third side, you can use the antilogarithm of a trigonometric function.

Let's assume we have a right triangle with an angle of 30 degrees and the lengths of the two sides adjacent and opposite to the angle are 5 units and 10 units, respectively.

1. Identify the trigonometric function that is relevant to the problem. In this case, it is the sine function because it relates the opposite side to the hypotenuse.

2. Write down the formula: sin(angle) = opposite/hypotenuse.

3. Substitute the known values: sin(30 degrees) = 5/10.

4. Rearrange the equation to isolate the unknown value (hypotenuse in this case). Multiply both sides of the equation by the hypotenuse: hypotenuse = (opposite/sin(angle)).

5. Now, we need to find the antilogarithm of sin(30 degrees) to evaluate the expression. To do this, we can use the exponential function with a base of 10 since most calculators have this function: hypotenuse ≈ 10^(sin^-1(5/10)).

6. Calculate the inverse sine (sin^-1) of (5/10): sin^-1(0.5) ≈ 30 degrees.

7. Substitute the value into the expression: hypotenuse ≈ 10^(30 degrees).

8. Finally, use a calculator to calculate the antilogarithm: hypotenuse ≈ 10^0.5 ≈ 3.16227766017 units.

Therefore, the length of the hypotenuse is approximately 3.162 units.

By using the antilogarithm and trigonometric functions, you can find the unknown values in triangles without relying on interpolation or log tables.