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algebra intermediate

Problem

Of the following (1)

a (x - y) = a x - a y

(2)

a^{x - y} = a^{x} - a^{y}

(3)

lo g (x - y) = lo g x - lo g y

(4)

\frac{l o g x}{l o g y} = lo g x - lo g y

(5)

a (x y) = a x \cdot a y

(A)

Only 1 and 4 are true

(B)

Only 1 and 5 are true

(C)

Only 1 and 3 are true

(D)

Only 1 and 2 are true

(E)

Only 1 is true

Solution

The distributive property doesn't apply to logarithms or in the ways illustrated, and only applies to addition and subtraction. Also,

a^{x - y} = \frac{a ^{x}}{a ^{y}}

, so

Only 1 is true

.

Final answer

E