Solving Logarithmic Functions Help

Subject Areas

Tools / Misc

bCalc

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scrnGC2: Calc Input

scrnGC3: f(x) Plot Input

scrnGC4: g(x) Plot Input

The inputs above will be hidden when the program finally gets launched. Currently, I am not hiding them even when you close the calculator. The purpose of the inputs is to help in debugging. This allows you to enter simple code on the calculator screen but the program translates the input to javascript math. Give it a try and see if you notice any obvious problems or have suggestions for improvements.

gCalc

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Select precision* of answer:

Select angle mode:

Enter expression to evaluate here:

The answer is shown below:

Enter function to be plotted:

f(x) =

Enter 2nd function, if needed:

g(x) =

Change or reset the x-y scaling below:

x_min =

x_max =

y_min =

y_max =

Accuracy Disclaimer

The javascript math object methods used for this calculator are not accurate for very large or very small numbers. In particular, the trigonometric functions may yield very small answers that should actually be zero or very large answers that should be infinite. This typically occurs at 90� or pi/2 intervals.

DO NOT USE WHERE HIGH PRECISION IS REQUIRED. USE AT YOUR OWN RISK.

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Solving Logarithmic Functions Help

Solving logarithmic functions requires knowledge of the logarithm properties and specifically, the identity property which simply states that if log(x) = log(y), then x must equal y. If you have an equation such as log(8) = log(2x), then x = 4. Sometimes, you may come up with more than one answer but usually you will find that one of the answers is not possible. Remember that y = log(x) is only defined for x > 0.

Example 1:   Given:     log ( x - 2 ) = log ( 5 )

x - 2 = 5

x = 7

Example 2:   Given:     ln ( x + 1 )² = 6

2 ln ( x + 1 ) = 6

ln ( x + 1 ) = 3

e ³ = x + 1 = 20.086

x = 19.086

Example 3:   Given:     log ( x + 1 )² = log ( 4 x )

( x + 1 )² = 4 x

x ² + 2 x + 1 = 4 x

x ² - 2 x + 1 = 0

( x - 1 ) ² = 0

x = 1

Example 4:   Given:     log ( x ² - 4 )= log ( 3 x )

x ² - 4 = 3 x

x ² -3x - 4 = 0

( x - 4 )(x + 1) = 0

x = 4     and     x = -1

x = 4     is only possible answer as log (-3) does not exist.