LOGARITHM WHAT FUNCTION ON THE TI 86 IS THE INVERSE LOG

Antilogarithm is equivalent to the inverse of a logarithm function.
Decimal (common) logarithm = log in base 10
Inverse of log in base 10: If y=log_10(x), then x=10^(y)
Natural logarithm (LN). If y=ln(x), then x=e^(y), e here is the exponential function.
As a rule (there may be exceptions) , calculators are designed so that a function and its inverse share the same physical key. One function is accessed directly the other is the SHIFTED key.

The inverse common logarithm is the shifted function of the "log" key, the inverse natural logarithm is the shifted function of the "ln" key.

The TI 86 has two logarithmic functions: natural logarithm (ln) and common (decimal) logarithms (log). If you need the logarithm in any other base than e or 10 you need to use one of the two equivalent expressions
log_b(x) =ln(x)/ln(b) =log(x)/log(b)
Here b is the value of the base of the logarithm and x is the argument (the value whose logarithm you are seeking). Of course the argument x must be a positive number.
Note: On the TI 86 the log function can calculate the logarithm of a complex number, according to the manual.

To take the log of a number, enter the number then press the LOG button, then the =. To take the log of a negative number, enter the negative number using the +/- key just to the right of the decimal point. To calculate the negative of a log, calculate the log and then negate it using +/-. To calculate the antilog (inverse logarithm), press 2nd then LOG.

Bear in mind that LOG is the common (base-10) logarithm. For the natural (base-e) logarithm, use the LN key to its right.

By 'log inverse', you presumably mean the inverse of the logarithm function. There are two logarithm functions on most scientific calculators. Firstly [ln], or natural logarithms, to the base e, where the inverse is e^x. Secondly [log], or logarithms to the base 10, where the inverse is 10^x.

Example 1 : ln(2) = 0.69314718 so e^0.69314718 = 2
Example 2: log(2) = 0.301029995 so 10^0.30102995 = 2

The inverse of the log function is the power function.
For log in base 10 that inverse is 10 to a power of
More generally, let b be the base of the logarithm. If y=log_b (x) then x=b^y
For your case log=log_10, to calculate the inverse you perform 10^(-2)=0.01=1/100
On calculators the log in base 10 and its inverse share the same physical key. One is accessed directly, the other is the shifted key function.

The inverse of the natural logarithm (in base e) is the EXPONENTIAL function (e^x). It shares the same physical key as the LN function. One is accessed directly and the other through the SHIFT key. The inverse of the logarithm in base 10 is the function 10^x. Both functions share the same physical key as described above.
More generally if y=log(in base b) of x =log_b(x) then x=b^(y). The base must of course be a non-zero positive number.

For the inverse natural log, press 2nd LN. For the inverse common log, press 2nd LOG.

For example, to calculate the inverse natural log of 2, press 2nd LN 2 ENTER and you'll get about 7.389 .

There are very few instances where you have two press two keys AT THE SAME TIME, the most notable of them is when you want to force the calculator into the BOOT SCREEN. Most key combinations are key sequences, meaning you press a key and THEN press another.

This said, let us get back to your question.

When you apply a function on an expression, then apply the inverse of the function on the result you get the original expression back.
If f is a function and f^-1 its inverse, by definition f^-1[f(x)]=f[f^-1(x)] =x
As you can see you do not need a calculator to find the result.

Concerning the logarithmic functions

For the natural logarithms (logarithms in base e) labeled [ln], the inverse of the logarithm is the exponential function e^
ln[e^(x)] =e^[ln(x)] =x

For the common logarithms (logarithms in base 10), labeled [log], the inverse function of the log is the raising 10 to the power of. It is usually called the antilogarithm or antilog.

y= log(x) is equivalent to x=10^(y)

Try the following exemple

log(14) = 1.146128036
10^(1.146128036) =14

To access the 10^x function you press [2nd][LOG]
To access the exponential function you press [2nd][LN]

Hello,
If you want to do correct mathematics you should strive to use the right words to express the concepts, and the right symbols too. While the logarithm function has an inverse function, it is never called an inverse log and it is never represented as log^-1. (I know you are going to protest and claim that the inverse of a sine function is represented on calculators by sin^-1. This a manufacturer shortcut, and we have no power to change that.) HP uses ASIN, ACOS, ATAN. These are still manufacturer shortcuts but they induce fewer errors.
Anyway, the logarithm functions do have inverse functions.

1. Natural loogarithm (ln)

The inverse of the natural log is the exponential.
ln(e^(x))=e^(ln(x)) =x

2. Common logarithm (logarithm in base 10)
The common logarithm has an inverse function, often called the antilogarithm or antilog.

There is an equivalence.
y=log(x) <--> x=10^(y)

From what I undesrtand of your exemple, you are looking for the antilog of the number -0.4/10 (or -0.04.)

-0.04= log(x), what is x?
You use the equivalence above to look for x as follows.
x=10^(-0.04) =0.9120108394.
Use the change sign (-) not the regular MINUS sign.

Take the log of the last result (still stored in Ans memory) and you get the original number.


Hope it helps.