Unit 5 Exponential and Logarithmic Functions Precalc Murphy

c to the nth root is also equivalent to

c to the one half n power

Product Rule

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

Quotient Rule

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

Power Rule

log (a^c) = c log (a)

#1 Rational Exponents Rule (c^ab)

(c^a)^b

So if #1 is true, can you switch the position of a and b?

Yes because the commutative property applies (five times two is the same as two times five)

a number (x) is multiplied by a single fraction (1/y) can simplify to

x/y

Solve 4^3/2

3/2 is also equal to 3 (1/2). According to the rational exponent law #1, the problem can be simplified to (4³)^1/2. 4³=64 and 64^1/2 is equal to sqr(64) final unrounded answer.

In radical notation, c^a/b

^bsqr(c)^a = (^bsqr(c))^a

Horizontal Asymptote

Specific spot on the graph that cannot have an y value (ex if you cross out on a fraction)