Can someone help me how to Simplify LOG4 16 it has no equals
and it is to base 4 since here it cannot be written in subscript!
2006-12-25 20:37:27 · 5 answers · asked by Amelie' 3 in Science & Mathematics ➔ Mathematics
Ok I know how to get the value of 2 but that's not eimplifying that's evaluating..or am I wrong?? and another question is: Express as a sum or difference of logs:
log(1/100ab2).
2 is supposed th be squared
2006-12-25 21:14:59 · update #1
if log a to the base b is x, then its the same as saying a = b^x.
here, 16 = 4^x, so x=2
Villach, perhaps what they mean in the question is 'use some basic property of log' in which case its better to do it as log to the base 4 of 4^2 which is 2 times 1 etc. But strictly speaking, log a to the base b is x is by definition same as a = b^x. But i know, math teachers can be irrational while giving marks (lol), so better to give them what they expect.
assuming its log to the base 10, log (1/100ab^2)
= - log(100 ab^2)
= -log(100) -loga -log(b^2)
=-log(10^2)-loga-2logb
=-2log10-loga-2logb
= -2 -loga -2logb
2006-12-25 20:46:04 · answer #1 · answered by Venkat 3 · 1⤊ 0⤋
well logs are a little tricky at first but once you get the hang of them they become quick simple. The easiest way to think of logs is to think of exponents. A log is basically the opposite of an exponent.
So log4 16: here you want to know what power the 4 needs to have to become 16.
so the simplified answer here is 2, because 4^2 (four squared)=16.
This is the same for all logs.
In order to perfrom an operation like this on your calculator you muct remember some basic log rules...
one such rule is that logx Y= (log Y)/(log X) ----where log is the common log, which has a base of 10.
2006-12-26 04:50:46 · answer #2 · answered by elucidiamia 2 · 0⤊ 0⤋
To simplify logarithms of this format log x (to the base y) or logy x we can write this as log y / log x. Hence, LOG4 16 can be written as log 16 / log 4 or log 16 divided by log 4. SO the answer is
log4 16 = log 16 / log 4 = 2
2006-12-26 06:49:59 · answer #3 · answered by Sheila 2 · 0⤊ 0⤋
log 16. Read log 16 to the base 4.
log 16
= log (4 x 4)
= log 4 + log4
= 2 log 4.
log 4 to the base 4 is 1.
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Second problem.
log (m x n) = log m + log n
log (m/n) = log m - log n
log (1/ 100 a b^2)
= log 1 - log 100 a b^2
But
log 100 a b^2 = log (100 x a x b x b)
= log 100 + log a + log b + log b.
=log 100 + log a + 2log b.
Therefore
log (1/ 100 a b^2)
=log 1 - {log 100 + log a + 2log b}.
=log 1 - log 100 - log a - 2log b.
2006-12-26 08:31:29 · answer #4 · answered by Pearlsawme 7 · 0⤊ 0⤋
log (base 4) 16 = log (base 4) 4²
= 2log (base 4) 4 = 2 * 1 = 2
2006-12-26 04:55:29 · answer #5 · answered by Northstar 7 · 0⤊ 1⤋