Exponential and Logarithmic Functions Reminder Sheet
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Exponential and Logarithmic Functions Reminder Sheet
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Exponential and Logarithm Rules Reminder Sheet Here are some facts you’ll be glad you remembered. Exponent Rules: (a & b are positive real numbers, x & y are real numbers) Write examples of each rule. Can you prove it in general? a x a y = a x+ y
ax = a x− y y a
(a )
= a xy
(ab )x
= a xb x
x y
x
ax a = x b b
If a ≠ 1, a x = a y ⇔ x = y If x ≠ 0, a x = b x ⇔ a = b If a ≠ 0 , a 0 = 1 Logarithm Rules: (a, x, y are positive real numbers, a ≠ 1 ) Write examples of each rule. Can you prove it in general? log a ( xy) = log a ( x ) + log a ( y ) log a
x = log a ( x ) − log a ( y ) y
( )
log a x y = y log a ( x )
You may not remember this, but it will come in handy when you are asked to graph y = log a ( x ) and a is not 10 or e.
log b x =
log c x log c b
Where c is any base you choose, (I’d choose 10 or e, since that’s what your calculator does by default)
( )
proof: log b x = A ⇒ b A = x ⇒ log c b A = log c (x ) ⇒ A log c (b) = log c (x ) ⇒ A =
