Simplify logarithmic and exponential expressions

for this I like to use logarithms to solve for N
reason 4 this is logarithms are the reverse of a exponential

log's have specific rules that exp's don't have to follow hence it makes it easier to solve for answers
using the formula logb(mn) = n · logb(m) will allow you to solve for N then just reverse the answer (do that in your head!!) and whhoollaaa! its an exponential !!!! neetooo

heres the log rules I was telling you about ! they apply to all log's uses

1) Multiplication inside the log can be turned into addition outside the log, and vice versa.

2) Division inside the log can be turned into subtraction outside the log, and vice versa.

3) An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.

I am not sure what model you are referring to. In general, to calculate natural logarithms you use the ln key. To calculate the exponential (e^x) you use [2nd] [LN] (e^x)
For decimal logarithms (logarithms in base 10) Use the [log] key. The inverse of the log(x) function is the power function 10^x. To access this function , use [2nd][log] (10^x).

That is the exponential function. Look for a key marked [LN] (the natural logarithm). The exponential function e^(x) shares the same physical key as the natural logarithm.
You access one function directly (marking on surface of key) and the other with [2nd] LN

That is the exponential function. Look for a key marked [LN] (the natural logarithm). The exponential function e^(x) shares the same physical key as the natural logarithm.
You access one function directly (marking on surface of key) and the other with [2nd] [LN]

Using logarithms. For example, if A ^ X = 2; then X = logA(2);
This calculator only works in base-10 logarithms or natural logarithms, you should use the base conversion formula.
logA(X) = logC(X) / logC(A).
Good luck!

The exponential function and the natural logarithm (LN) are inverse of one another. They share the same physical key. To calculate the natural log [LN] press the key marked LN and enter the number. Close the parenthesis) and press [=]
To calculate the exponential, use the key combination [SHIFT][LN] followed by the number.

The inverse of a natural logarithm (ln) is the exponetial (e^x). Both share the same physical key [LN] pour ln and [SHIFT] [LN] (e^x) for the exponential.
Syntax is : [ln] 3 [EXE] gives 1.098612289
exponential of 4: [SHIFT][LN] 4 [=] 54.59815003

The inverse of decimmal logarith is raise 10 to a power. Both share tha same physical key [LOG]
log of 6 : [log] 6 [=] result is 0.7781512504
antilog of 0.77: [SHIFT][LOG] 0.77 [=] result is 5.888436554

For more complicated arguments (expressions) it may be a good idea to use parentheses to enclose the arguments of functions.

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]

Hi,
Sorry to contradict you but there are many types of logarithms, the most important ones are

1. the common logarithms (log in base 10),
2. the natural logarithms (logarithms in base e)
3. the binary logarithms (logarithms in base 2)

On calculators, the common logarithms are labeled [LOG], and the natural logarithms are labeled [LN].

The inverse function of the natural log function is the exponential (e^(x)), and the inverse of the log in base ten function is the function ten to the power of. It is called (sometimes) the antilog

Ex:
Question What is the antilog of 3.5678?
Answer The antilog of 3.5678 is 10^(3.5678) = 3696.579068
Verification: log(3696.57908) =3.5678

Hope it helps.

Hello,
There is no key dedicated to e, the base of natural logarithm, the same as there is for pi. However you can find it as the VALUE of the exponential function e^(x) for x=1. To obtain the VALUE of e you press [SHIFT] [ln] to access e^x, enter 1 and press [EXE].

Thus
[SHIFT][LN]1 [EXE] gives 2.718281828.

If you need that numerical VALUE often you may want to store it into a variable, say E. To do that
[SHIFT][LN]1 [-->] [APLHA] E [EXE]

From experience, I know that it is not the VALUE of e that you need but the symbol e to define the exponential function. If you press [SHIFT][LN] you get a syntax error. You can never see e in a multiplication, addition, or other arithmetic operation.

In this calculator, the e is first and foremost the symbol for the exponential function. If you need to draw the exponential function of X
you press [SHIFT][LN] X. Parentheses are not needed for simple arguments as this one, but if the exponent is a complicated expression parentheses are needed.
If you mean exponential of X you type [SHIFT][LN] [X,theta,T], but if you want exponential of (x-3z+ 0.5 y^2), you must enclose the argument (the object of the function) between parentheses
[SHIFT][LN] [ ( ] x-3*z+ 0.5*y [^]2 [ ) ] [EXE].

Hope it helps.