# Shared Flashcard Set

## Details

Logarithms Part II
Better set of flashcards on logs
26
Mathematics
08/28/2009

Term
 How do you re-write logbA = x in exponent form?
Definition
 bx = A Example 1: If given log28 = x, you would rewrite it in exponent form as 2x = 8.   Example 2: If given log39 = x, you would rewrite it in exponent form as 3x = 9   Example #3: If given log5125 = x, you would re-write it in exponent form as 5x = 125
Term
 What is exponent form?
Definition
 bx = A An equation is in exponent form when you have a base raised to an unknown power.   Example 1:               6x = 36  Example 2: 3x = 27
Term
 What is logarithmic form?
Definition
 logbA = x Logarithmic form is when the exponent is the result. The word "log" is just an instruction that tells you what to do (solve for the exponent).
Term
 Identify each part of the following equation in exponent form:   bx = A   1) What is the exponent? 2) What is the base? 3) What is the result?
Definition
 1) x 2) b 3) A
Term
 Identify each part of the logarithm:   logbA = x   1) What is the base? 2) What is the exponent? 3) What is the "result"?
Definition
 1) b 2) x 3) A
Term
 How are logbA = x and bx = A related?
Definition
 They are two ways of expressing exponents. Sometimes it is easier to see the answer if you re-write a log into an exponent.
Term
 How do you expand logb(a·c)?
Definition
 logba + logbc   Rewrite it as the sum of two logarithms. Both logarithms have the same base, but they have different "results".   Note: If you had logb(a·c·d), you would write is logba + logbc + logbd
Term
 How do you expand logb(a/c)?
Definition
 logba - logbc   Rewrite as the difference of two logs. Both logs have the same base, but different "results".
Term
 How do you expand logbAP?
Definition
 P·logbA logbAP is logbA raised to the power P. To re-write it move P to the front of the log and multiply the log by P.
Term
 How do you re-write lnA so that it looks like a regular logarithm (so it is in the form logbA)?
Definition
 logeA   In this situation, e is Euler's number, not a variable. So, the base is e.
Term
 Re-write lnA = x in exponent form
Definition
 ex = A   Ln means a log with base e.
Term
 What is euler's number?
Definition
 Euler's number is a mathematical constant like pi. It roughly equals 2.71828 18284 59045 23536. It is represented by the lower case letter e.
Term
 If given log100 = x, what base is implied?
Definition
 Base 10 is implied. For example, log100 = x, is log10100 = x If you are given log2 = x, base ten is still implied. So, log2 = x can be re-written as log102 = x
Term
 Do logA and lnA have the same implied base?
Definition
 NO! Both logA and lnA have implied bases, but the implied base of logA is 10 and the implied base of lnA is e.
Term
 What is the change of base formula, and what does it do?
Definition
 The change of base formula is: logbA = lnA / lnb   The change of base formula lets you re-write a log of any base, b, into a natural log (a log of base e, or ln)
Term
 Say you're given log28 = x. What is the value of x? (Rewrite in exponent form first, then solve for x)
Definition
 log28 = x re-written in exponent form: 2x = 8 x = 3
Term
 Say you're given log636 = x. What is the value of x?
Definition
 log636 = x re-written as in exponent form: 6x = 36 x = 2
Term
 If given log4(3·a), how do you expand it?
Definition
 log43 + log4a
Term
 If given log9(4·500), how do you expand it?
Definition
 log94 + log9500
Term
 If given log8(ab), how do you expand it?
Definition
 log8a + log8b
Term
 If given log7(49/343), how do you re-write it?
Definition
 log749 - log7343
Term
 If given log3(a/9), how do you re-write it?
Definition
 log3a - log39
Term
 If given log2(8/a), how do you expand it?
Definition
 log28 - log2a
Term
 If given log4(a/b), how do you expand it?
Definition
 log4a - log4b
Term
 If given log392, how do you expand it?
Definition
 2log39
Term
 If given log216a, how do you expand it?
Definition
 alog216
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