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What do these pairs have in common?
sin and sin-1 + and -
÷ and •
cos and cos-1
tan and tan-1
2and
inverses
Introducing… Logarithms!
A logarithm is defined as follows:
If y = bx, then logb y = x
x is now safely on the ground!
Okay, we can get x down from the exponent, but what do we do with an expression like this?
log10 100 = x Your calculator automatically uses
log10 when we press the LOG function the
calculator. Try it!
How does this help us?
Change of Base Formula
What if we have an expression that doesn’t have a base of 10?
log9 81 = xChange of Base
Formula
log9 81 = 9log
81log
10
10
So what undoes x when it’s an exponent?
y = a b∙ x
Yesterday, we learned how to solve for a variable when it is an
exponent.
Get me down!
What do we do if we have a variable trapped in a log?
So what undoes x when it’s an exponent?
log4 x = 78 Get me out
of here!