Yahoo Answers: Answers and Comments for Why does log 10 100,000 equal to 5?
Why must log 10 5 be a number between 0 and 1? [Mathematics]
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From Blain
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Thu, 12 Dec 2019 21:49:59 +0000
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Yahoo Answers: Answers and Comments for Why does log 10 100,000 equal to 5?
Why must log 10 5 be a number between 0 and 1? [Mathematics]
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From skeptik: A logarithm (log) is the exponent a number (ba...
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Thu, 12 Dec 2019 22:08:49 +0000
A logarithm (log) is the exponent a number (base) must be raised to in order to equal another number.
10^5 = 100,000
So 5 is the base10 log.
Also, any number raised to the power of 0 = 1.
And any number raised to the power of 1 = the number itself.
So, 10^0 = 1. And 10^1 = 10
Since 5 is between 1 and 10 (or between 10^0 and 10^1), its base10 log must be between 0 and 1.

From Jim Moor: Because 10^5 = 100,000
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Thu, 12 Dec 2019 22:05:53 +0000
Because 10^5 = 100,000

From Iggy Rocko: log(base 10)100000 = 5 because 10^5 = 100000
...
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Thu, 12 Dec 2019 23:45:20 +0000
log(base 10)100000 = 5 because 10^5 = 100000
10^0 = 1
10^1 = 10
1 < 5 < 10
Therefore, 0 < log(base 10)5 < 1.

From Daniel H: rule 1: log[base a](b^c) = c log[base a](b)
ru...
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Thu, 12 Dec 2019 23:39:11 +0000
rule 1: log[base a](b^c) = c log[base a](b)
rule 2: log[base a](a) = 1
rule 3: log without base written is assumed to be base 10
log(100,000) = log(10^5) = 5log(10) = 5

From L. E. Gant: 100,000 = 10^5
100000 = 10^(log(100000))
so, ...
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Thu, 12 Dec 2019 22:46:19 +0000
100,000 = 10^5
100000 = 10^(log(100000))
so, log(100000) = 5
For the other part:
10^0 = 1 ==> log(1) = 0
10^1 = 10 ==> log(10) = 1
1 < 5 < 10
so log(5) must be between 0 and 1

From llaffer: Why does log₁₀(100000) equal 5?
When the base...
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Thu, 12 Dec 2019 21:54:41 +0000
Why does log₁₀(100000) equal 5?
When the base of the log and the base of the number inside are the same, they cancel each other out leaving only the exponent. So putting your number into a power of 10 we get:
log₁₀(100000)
log₁₀(10⁵)
The 10's cancel out leaving only:
5

Why must log₁₀(5) be a number between 01?
Because the log of any base of 1 is 0, because the 0th power of any nonzero base is 1. Using the example above we can say:
log₁₀(10⁰) = 0
log₁₀(1) = 0
So the log of 1 from any base is 0.
To get the log to equal 1, the value inside needs to be 10:
log₁₀(10¹) = 1
Since 5 is between 10⁰ and 10¹, the log of 5 is between 0 and 1.

From Como: Definition
The log of a number to a given base...
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Sat, 14 Dec 2019 18:23:24 +0000
Definition
The log of a number to a given base is the index of the power to which the base must be raised in order to give the number.
Examples
1000 = 10³
log 10 (1000) = 3
16= 2⁴
log 2 (16) = 4
Thus
100 000 = 10^5
log 10 (100 000) = 5

From Alexandros: log 10 100,000
log 10 (10)^5
= 5
10 base
100...
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Sat, 14 Dec 2019 03:08:03 +0000
log 10 100,000
log 10 (10)^5
= 5
10 base
100,000 final product
5 power
Logarithms (without the given base) are done in 10s

From Suman: Knowing some basic facts, log 1=0 and log10= 1...
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Sat, 14 Dec 2019 01:12:23 +0000
Knowing some basic facts, log 1=0 and log10= 1
we can write
log100= log10^2 = 2 log10=2*1=2
log1000= log10^3= 3log10 =3*1=3
log10000=log10^4=4 log10=4*1=4
log100000= log10^5= 5log10=5*1=5
and so on....
basically number of zeros tells the value of log.
We know that log1=0 and log10=1 so log values of all the numbers lying between 1 and 10 would lie between 0 and 1.
Based on this we can say that log5 would also be a number between 0 and 1
https://celestialtutors.com/topic/exponentialandlogarithmicfunctions/

From jeffdanielk: Log base 10 of a number means 10 raised to wha...
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Fri, 13 Dec 2019 04:03:46 +0000
Log base 10 of a number means 10 raised to what power will give you that number.
10^5 = 100,000
So that exponent, 5, is the Log of 100,000

From Anonymous: log(10) 100,000 = log(10)10^5 = 5
log(10) 5 wo...
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Thu, 12 Dec 2019 22:03:13 +0000
log(10) 100,000 = log(10)10^5 = 5
log(10) 5 would be found in the interval log(10)1<log(10)5<log(10)10 or log(10)10^0 <log(10)5 <log(10)10^1 or 0<log(10)5<1

From Anonymous: Because it just is
.
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Thu, 12 Dec 2019 21:51:07 +0000
Because it just is
.