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How do you re-write
logbA = x in exponent form? |
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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 |
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Term
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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 |
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Term
| What is logarithmic form? |
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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). |
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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? |
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Definition
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Term
Identify each part of the logarithm:
logbA = x
1) What is the base?
2) What is the exponent?
3) What is the "result"? |
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Definition
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Term
How are
logbA = x and bx = A related? |
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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. |
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Term
How do you expand
logb(a·c)? |
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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 |
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| How do you expand logb(a/c)? |
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Definition
logba - logbc
Rewrite as the difference of two logs. Both logs have the same base, but different "results".
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Term
How do you expand
logbAP? |
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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.
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Term
| How do you re-write lnA so that it looks like a regular logarithm (so it is in the form logbA)? |
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Definition
logeA
In this situation, e is Euler's number, not a variable. So, the base is e.
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| Re-write lnA = x in exponent form |
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Definition
ex = A
Ln means a log with base e.
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Term
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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.
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Term
| If given log100 = x, what base is implied? |
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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
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Term
| Do logA and lnA have the same implied base? |
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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. |
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| What is the change of base formula, and what does it do? |
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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) |
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Term
Say you're given log28 = x. What is the value of x?
(Rewrite in exponent form first, then solve for x) |
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Definition
log28 = x re-written in exponent form:
2x = 8
x = 3
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| Say you're given log636 = x. What is the value of x? |
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Definition
log636 = x re-written as in exponent form:
6x = 36
x = 2 |
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| If given log4(3·a), how do you expand it? |
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Definition
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| If given log9(4·500), how do you expand it? |
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Definition
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| If given log8(ab), how do you expand it? |
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Definition
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| If given log7(49/343), how do you re-write it? |
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Definition
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| If given log3(a/9), how do you re-write it? |
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Definition
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| If given log2(8/a), how do you expand it? |
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Definition
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| If given log4(a/b), how do you expand it? |
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Definition
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| If given log392, how do you expand it? |
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Definition
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| If given log216a, how do you expand it? |
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Definition
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