Question 384372: **Logarithms are mainly used to solve exponential equations.
**In words, the expression a b log represents ___________________________.
**We can convert an equation in log form, y a b = log to an equivalent exponential form ______________.
**The most frequently used bases for logarithms are ________ and ____________.
**3 commonly used log properties: _____________, _______________, ______________
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a b log means the log of a to the base b as far as I know.
this is written as log(b,a) which means the log of a to the base b.
y a b log means y = log of a to the base of b.
This is written as y = log(b,a) which means that y is equal to the log of a to the base of b.
The conversion of a log expression to an exponential expression is given by the equation of:
b^y = a if and only if log(b,a) = y
This means that the base b raised to the power of y is equal to a if and only if the log of a to the base b is equal to y.
Likewise, the conversion of an exponential expression to a log expression is given by the equation of:
log(b,a) = y if and only if b^y = a
An example is as follows:
We know that 10^3 is equal to 1000.
By the equation of b^y = a if and only if log(b,a) = y, we should be able to see that:
10^3 = 1000 if and only if log(10,1000) = 3
Since the LOG function of our calculator can give us the log of 1000 to the base of 10, we can easily see that log(1000) = 3.
You just enter 1000 into the calculator and then hit the log key. It should return a value of 3.
This assumes you have a calculator like the Texas Instruments or one with equivalent functionality.
The most frequently used bases for logs are 10 and LN.
LN stands for natural log.
the LOG function of the calculator does logs to the base of 10.
The LN function of the calculator does logs to the base of e.
the base of e is equivalent to the base of 2.718281828... because the letter e represents that value.
The value of the base e is used a lot in scientific studies.
3 commonly used log properties are:
log(a*b) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(a^b) = b*log(a)
log(a) implies the base of 10, and can also be written as log(10,a).
There is also a conversion formula that you can use to translate the log of any base to the base of 10 or e, so that the log can be solved using your calculator.
That formula is:
log(b,a) = log(c,a) / log(c,b)
This means that the log of a number to the base of b is equivalent to the log of that same number to the base of c divided by the log of the base b to the base of c.
An example will clarify:
You start with log(2,8)
We know that log(2,8) = 3 because 2^3 = 8
Suppose we didn't know that.
We could find it by converting to the base of 10.
log(2,8) = log(10,8) / log(10,2)
Use your calculator to find log(8).
Use your calculator to find log(2).
divide log(8) / log(2) and you should get 3.
Works every time and is a very useful tool if you have logs in unfamiliar bases and you want to use your calculator to solve them.
You can also do the same thing with the LN function of your calculator.
log(2,8) = ln(e,8) / ln(e,2)
Use the LN function of your calculator to find LN (8).
Use the LN function of your calculator to find LN (2).
Divide ln(8) by ln(2) and you should also get 3.
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