Exponents 

Base^exponent= Answer

the base and exponent can be any real number

D:   all real numbers

the answer must be positive

R:   y: y > 0   

Exponent Rules 

If the bases are the same: 

To multiply, add the exponents

(x⁴)(x⁵) = x⁹        

To divide, subtract the exponents

Power of a power, multiply the exponents 

(a⁷)³ = a²¹           

Logarithms 

log_baseAnswer = Exponent

log_baseargument= answer

the base and argument have to be positive

D:   x: x > 0

the answer can be any real number

R:   all real numbers  

Log Rules 

If the bases are the same: 

Multiplying can be split into adding 

log_bMN = log_bM + log_bN 

Adding logs of the same base can be combined into multiplying the arguments 

log_bM + log_bN = log_bMN   

Dividing can be split into subtracting 

log_b(M/N) = log_bM - log_bN 

Subtracting with the same base can be combined into dividing the arguments

log_bM - log_bN = log_b(M/N)    

Power of a log can be changed to multiplying 

log_bM^k = k log_bM 

Multiplying a number times a log can be changed to a power of the log

log k log_bM = log_bM^k    

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