Exponents
An exponential function is a function that involves repeated multiplications of something by itself. The most basic exponentional function can be expressed as a^n=b where a is any positive number that is being multiplied and n is the number of times a is multiplied by itself. a is called the base; n is called the exponent, and b is called the power. a^n= a*a*a*a(n number of times)= b
Properties of exponentials
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(x^a)*(x^b)=x^(a+b)
(x^a)/(x^b)=x^(a-b)
(x^a)^b=x^(a*b)
a^(-n)}&=1/(a^n)
x^0=1
x^(a/b)=sqrt[b](x^a)
if a^x=a^y then x=y
Example
Take 2^4. This exponential can be re-written as 2*2*2*2 = 4*2*2=8*2=16
Thus:2^4=16
Logarithms
Logarithms are the "opposites" of exponentials. They are used to undo exponential functions. Logarithmic expressions are written in the form: log'a(b)=c where a is what is called the base of the logarithm, b is the antilogarithm, and c is the logarithm. ( ' will stand for subscript)
Properties of Logarithms
log'b(a)+log'b(c)=log'b(a*c)
log'b(a)-log'b(c)=log'b(a/c)
log'b(a^c)=c*log'b(a)
Logarithms and Exponents Practice Problems
Solve log'x(49)=2
By the property of logarithms and exponents, we can rewrite the equation as: 49=x^2, and so sqrt49=x, 7=x.