0
log0.1 50 = log10 50 / log10 0.1
~= -1.699
To work out the log to any base b, logs to another base can be used:
When logs are taken of a number to a power, then the power is multiplied by the log of the number, that is:
log(bn) = n log b
Taking logs to base b the power of b that equals the original number is being found, that is if:
bn = m
then
logb m = n
So, by using the logs to a base to which the answer can be known, the log to any base can be calculated:
bn = m
=> n log b = log m
=> n = log m / log b
=> logb m = log m / log b
as long as the same base is used for the logs on the right. It is normal to use base 10 or base e which are found on calculator buttons marked log (base 10) and ln (log natural - base e).
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Log base 2 of x - log base 2 of x-23?
log base 2 of [x/(x - 23)]
Can the base of a logarithm be 0?
No, it is undefined and indeterminate. Log base y of a variable x = N y to the N power = x if y ( base) = 0 then 0 to the N power = x which is always zero (or one in some cases) and ambiguous. Say you want log base 0 of 50 0 to the N power = 50 cannot be true as 0 to the N is always zero
Log base 3 of 81 plus log base 3 of 81?
Log base 3 of 81 is equal to 4, because 3 ^ 4 = 81. Therefore, two times log base 3 of 81 is equal to 2 x 4 = 8.
Which logarithm is equivalent to log base 3 16 - log base 3 2?
log316 - log32 = log38
How do I solve the equation e to the power of x equals 2 using logarithms?
When the logarithm is taken of any number to a power the result is that power times the log of the number; so taking logs of both sides gives: e^x = 2 → log(e^x) = log 2 → x log e = log 2 Dividing both sides by log e gives: x = (log 2)/(log e) The value of the logarithm of the base when taken to that base is 1. The logarithms can be taken to any base you like, however, if the base is e (natural logs, written as ln), then ln e = 1 which gives x = (ln 2)/1 = ln 2 This is in fact the definition of a logarithm: the logarithm to a specific base of a number is the power of the base which equals that number. In this case ln 2 is the number x such that e^x = 2. ---------------------------------------------------- This also means that you can calculate logs to any base if you can find logs to a specific base: log (b^x) = y → x log b = log y → x = (log y)/(log b) In other words, the log of a number to a given base, is the log of that number using any [second] base you like divided by the log of the base to the same [second] base. eg log₂ 8 = ln 8 / ln 2 = 2.7094... / 0.6931... = 3 since log₂ 8 = 3 it means 2³ = 8 (which is true).
How do you calculate the exponent y if the base is 2 and the answer is 50?
If 2y = 50 then y*log(2) = log(50) so that y = log(50)/log(2) = 5.6439 (approx). NB: The logarithms can be taken to any base >1.
What is the exponential notation of 50?
Find log of 50, this becomes power on base 10, so, 10 1.69897 = 50
Suppose aneq 0. Compute log 2a 2b in terms of a and b.?
Due to the rubbish browser that we are compelled to use, it is not possible to use any super or subscripts so here goes, with things spelled out in detail: log to base 2a of 2b = log to base a of 2b/log to base a of 2a = [(log to base a of 2) + (log to base a of b)] / [(log to base a of 2) + (log to base a of a)] = [(log to base a of 2) + (log to base a of b)] / [(log to base a of 2) + 1]
What is log 100 base e?
log 100 base e = log 100 base 10 / log e base 10 log 100 base 10 = 10g 10^2 base 10 = 2 log 10 base 10 = 2 log e base 10 = 0.434294 (calculator) log 100 base e = 2/0.434294 = 4.605175
Log base 2 of x - log base 2 of x-23?
log base 2 of [x/(x - 23)]
What is the log of infinite to the base 10?
The log of infinity, to any base, is infinity.
What is the same thing as log base e?
log base e = ln.
Can the base of a logarithm be 0?
No, it is undefined and indeterminate. Log base y of a variable x = N y to the N power = x if y ( base) = 0 then 0 to the N power = x which is always zero (or one in some cases) and ambiguous. Say you want log base 0 of 50 0 to the N power = 50 cannot be true as 0 to the N is always zero
What is the log of 40000?
It is the value that when the base you have chosen for your log is raised to that value gives 40,000 log with no base indicated means log to any base, thought calculators often use it to mean logs to base 10, which is often abbreviated to lg lg(40,000) = log{base 10} 40,000 ≈ 4.6021 ln(40,000) = log{base e} 40,000 ≈10.5966
What is the value of log 50?
Very simple: it is 1.6989700043 to be exact. You can test this because log50 means we assume the natural log (base 10), if you test 10 to the exponent of 1.6989700043 you should render 50 as your result :D
What number has a log of 8.0573-10?
18.057299999999998
What is log base 3 of (x plus 1) log base 2 of (x-1)?
The browser which is used for posting questions is almost totally useless for mathematical questions since it blocks most symbols.I am assuming that your question is about log base 3 of (x plus 1) plus log base 2 of (x-1).{log[(x + 1)^log2} + {log[(x - 1)^log3}/log(3^log2) where all the logs are to the same base - whichever you want. The denominator can also be written as log(3^log2)This can be simplified (?) to log{[(x + 1)^log2*(x - 1)^log3}/log(3^log2).As mentioned above, the expression can be to any base and so the expression becomesin base 2: log{[(x + 1)*(x - 1)^log3}/log(3) andin base 3: log{[(x + 1)^log2*(x - 1)}/log(2)
