Title: InkMaths / Indices and log laws
On every note of this deck, unless a note says otherwise:
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Front: STANDARD RESULT — LEARN IT
Quotient law:
log_a x − log_a y = ?
Back: log_a x − log_a y = log_a xy

Front: STANDARD RESULT — LEARN IT
Power law:
k log_a x = ?
Back: k log_a x = log_a (x^k)

Front: SPOT THE ERROR
Say what is wrong with this claim:
log(x + y) is the same as log x + log y.
Back: The product law says log x + log y = log(xy): logs turn products into sums, not sums into sums. log(x + y) does not simplify. Try x = y = 10: log 20 is about 1.3, but log 10 + log 10 = 2.

Front: CHECK YOURSELF
Write 2 log 3 + log 4 as a single logarithm.
Back: 2 log 3 = log 9, and log 9 + log 4 = log 36.

Front: STANDARD RESULT — LEARN IT
Product law:
log_a x + log_a y = ?
Back: log_a x + log_a y = log_a (xy)

Front: DEFINE
Define: logarithm.
Back: log to base a of x is the power to which a must be raised to give x: if a^y = x then y equals log base a of x, for a > 0, a ≠ 1 and x > 0.