Unit 4 Flashcards
Log rule one - product rule
The logarithm of the product of numbers is the sum of logarithms of individual numbers.
Log rule two- quotient rule
The logarithm of the quotient of numbers is the difference of the logarithm of individual numbers.
Log rule three - power rule
The logarithm of an exponential number is the exponent times the logarithm of the base.
Log rule four - zero rule
The logarithm of 1 with b > 1 equals zero.
Log rule five - Identity rule
The logarithm of a number that is equal to its base is just 1.
Log rule six - log of exponent rule
The logarithm of an exponential number where its base is the same as the base of the log equals the exponent.
Log rule seven - Exponent of log rule
Raising the logarithm of a number by its base equals the number.
How to solve :
LogbM + LogbN
( when bases are the same )
Express M and N as exponential numbers with base b. Then, apply Power Rule followed by Identity Rule. After doing so, you add the resulting values to get your final answer.
logbM = N is equivalent to -
B^N= M
If you have a single logarithm on each side of the equation having the same base then you can -
set the arguments equal to each other and solve.
If you have a single logarithm on one side of the equation then you can -
express it as an exponential equation and solve.
True or false
It is OKAY to have values of x such as positive, 0, and negative numbers.
True
True or false
it is NOT ALLOWED to have a logarithm of negative number and zero when substituted or evaluated into the original logarithm equation.
True
If you see “log” without an explicit or written base, it is assumed to have a base of
- In fact, logarithm with base 10 is known as the common logarithm.
Parts of a logarithm
Log(base)(answer)=(argument)
