How do we use Logarithms?

We use logarithms in the case where we know what a number raised to a power equals, but we do not know what power that number was raised to.





To use logarithms we harness the term "log" in which case if we wanted to know the logarithm of 3 to the x power, we would simply input a "log" in front of the 3 to the x power.





However in an equation like 3 to the x power equals 729, we would do the logarithm of 3 to the x power and 729.





Once we take the Log of 3 to the x power, we bring down the x as a coefficient. We could do the same for Log of 729, but it would be a waste of time because 729 is raised to the 1st power, and 1 times any number equals the number itself.









Then once we've accomplished that we divide each side by Log of 3 to discover what x equals.













Another Example of Usage of Logarithms











What exactly are Logarithms?

A logarithm is the opposite, more commonly known as inverse, of exponents. The general equation associated with logarithms is:



Which translates into:



When graphing a logarithm, the b must always equal 10. If there is no number registered for "b" in a logarithm formula, then we assume that b=10. However we use b^m=n when b is any number but 10.

To make b^m=n into a graphing form, when b does not equal 10, we:













Naima Holland
#10
FX-63
a. 2(x+3)=64
64=2x2x2x2x2x2
64=26
2(x+3)=26
x+3=6
subtract 3 from both sides.
x=3
b.8x=46
8=2x2x2x2
8x=(23)x=23x
4=2x2
46=(22)6=212
23x=1212
3x=12
divide 3 by both sides
x=4

c.9x=1/27
9=3x3
9x=(32)x=32x
27=3x3x3
1/27=1/33=3-3
32x=3-3
2x=-3
divide each side by 2
x=-1.5 or =3/2

Problem Topic:
Solving equations and logarithms
Notes:
The first type of logarithmic equation has two logs, each having the same base, set equal to each other, and you solve by setting the insides (the "arguments") equal to each other.