Can someone explain logs to me? log 32/ log 4?

Question

We are not allowed to use calculators in class. So how can I solve that? Is there a trick? Id greatly appreciate ANY help.

If you could apply your rule to log 16/ log 4 (which equal two)...Id be real happy.

Thanks!

Answer 1

log32=log(2^5) = 5 x log2
log4 =log(2^2) = 2 x log2

log 32/ log 4 = (5 x log2) / (2 x log2) = 5/2 = 2 1/2
No calculator used. Only rules.
Take care you learn the rules well!

Th

Answer 2

Log is like a machine stamper. It has one function in life. To tell ou how many base units are needed to mutliple by each other to make a number. The answer or break down if you will is also called exponents.
Example 100 is 10 x 10
so the log(base 10) of 100 = 2

We know that 10,000 is 100 *100 there fore
10,000 is 100 squared or it
would take 2 more tens to make 10,000 than 100.

log 10000 = log 100^2 = 2 log 100 = 4

now for
log 16 = 2 log 4 when divided by log 4 the amswer is 2.

Answer 3

A few ways to look at it:
(1) The value of log N will be the answer to the question "what power of the base is N?" Often the base is assumed to be 10, so to find log 100 you'd ask "what power of 10 is 100?" Well, that's 2, simply.

(2) The log (with any base) of a number raised to a power can be determined by "pulling out" the power to the outside: log (a^b) = b * log (a).

(3) For quotients, you can use fact 2 above to get a common logarithm in the numerator and denominator and cancel these out: write both 32 and 4 as powers of the *same* number, and pull out the exponents. Well, 32 and 4 are both powers of 2, so log(32)/log(4) = log(2^5)/log(2^2) = (5*log(2))/(2*log(2)). Then the logarithms cancel and you get 5/2. That's all there is to it. Just remember, find a way to express both numbers as the power of the same number, then pull out exponents.

For your 2nd example, then, 16 and 4 are both powers of 4:
log(16)/log(4) = log(4^2)/log(4^1) = (2*log(4))/(log(4)) = 2.

Answer 4

For one thing, log(32)/log(4) is the same as log[base 4](32). This is by the change of base formula.

All you have to do is reapply the change of base formula and make it base 2.

log[base 4](32) = log[base 2](32) / log[base 2](4)

2 to the what is 32? The answer is 5.
2 to the what is 4? The answer is 2.

Therefore,

log[base 4](32) = log[base 2](32) / log[base 2](4)
= 5/2

Answer 5

1000 = 10³ so log 1000 = 3----------(in base 10)
5² = 25 so log 25 = 2------------(in base 2)

In given question, use base 2:-

Note that 32 = 2^(5) , 4 = 2², 16 = 2^(4)

log 32 / log 4 = 5/2

log 16 / log 4 = 4/2 = 2

Answer 6

log32/log4 = log(2)5 means 2 to the power of 5
divided by log(2)2
log2 and log 2 gets cancelled.So the answer is 5/2
What I advise is know the properties of logarithms correctly.
I have done this problem using log(m)n = nlogm.
log m to the power of n = nlogm

Answer 7

it fairly is elementary.. log(base 4)32 = ln 32 / ln 4 = ln(2^5)/ln(2^2) = (5*ln2)/(2*ln2) = 5/2. log(base 9)27 = ln 27/ln 9 = ln(3^3) / ln(3^2) = 3* ln3 / 2* ln 3 = 3/2 for this reason the respond is = (5/2) - (3/2) = a million. wish this helped. :)

Answer 8

log 32 / log 4
= log 2^5 / log 2^2
= 5log 2 / (2log 2)
= 5/2
----------
Or
log 32 / log 4
= log 16^(5/4) / log 4
= (5/4) log 16 / log 4
= 5/2

Answer 9

log(a^n) = n log (a)

32 = 2^5
4=2^2

16= 2^4

(log 16)/ (log 4 ) = log(2^4) / log(2^2) = [4 log2] / [2 log2 ] = 2

Answer 10

Log16/log4=log4+log4/log4 =1+1=2
...Lo32/log4=log4+log8/log4=1+log8/log4=1+(log2+log4)/log4=
=1+1+log2/log4=2+1/2=(4+1)/2 =5/2