Algebra II Final Part 3: Inverses and Logarithms (ASSUME ALL NUMBERS/ VARIABLES AFTER LOG NOT IN PARENTHESIS ARE THE BASEEEEEEE)

Includes graphing an inverse function, creating an inverse equation, evaluating logarithms, and using tables with logarithms

Graph the inverse given the initial graph and the line of y=x

Properties of log: Rewrite logb(xy)

logb(x)+logb(y)

Properties of log: logb(x^y)

ylogb(x)

Properties of log: logb(x/y)

logb(x)-logb(y)

Evaluate 6^log6(5)

5
(if the number and the log’s base are the same, the other number will be the answer)

Evaluate: log8(1/8)

-1

(rather than use the property of log here, rewrite 1/8 as its equivalent, 8^-1. Since the log base and the exponent base are now the same (8), we simply take the exponent as the answer, -1)

Evaluate:

1/5
(with radicals, we can take the top number in the radical (5 in this case) and use it as a numerator and use the exponent of the number inside (1 in this case) as the numerator, making 1/5. We rewrite everything as log4(4^1/5). As said before, if the log and exponent bases are the same, simply use the exponent as your answer).

If you are given a log without a base, what base is it assumed to be (in the U.S, at least)?

log10

If I wanted to do log15(20), but only had a log10 table, what could I do?

Do log10(20)/log10(15), as they are equivalent. This is also how you use the log button in your calculator. This method works with any log base, not just log10.