Logarithms

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Convert to exponential form. log4 (4) = x

4^x = 4

True or False? (log a)(log b) = log(a + b)

False

True or False? log(a − b) = log a − log b

False

Product property

log(x)+log(y)=log(xy)

Quotient property

log(x)-log(y)=log(x/y)

One-to-one property

log(x)=log(y), so x=y

Convert to logarithmic form. 8^2 = 64

log8 (64) = 2

Convert to logarithmic form. x^2z = y

logx (y)/2 = z

Logarithmic form is the inverse of exponential form.

True

Find the inverse of the following equations. f(x) = log2 (x − 3) − 5

f −1 (x) = 2x + 5 + 3

Solve log(x) + log(x-1) = log(3x+12)

x = -2, 6

Convert to exponential form. logx (y) = z

x^z = y

Find the value of y. log5 (25) = y

y = 2

Find the value of y. logy (16) = 2

y = 4


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