For a quotient x/y , then its log is logx - log y . NOT log(x/y)
y = 10 y = log x (the base of the log is 10, common logarithm) 10 = log x so that, 10^10 = x 10,000,000,000 = x
An exponential function can be is of the form f(x) = a*(b^x). Some examples are f1(x) = 3*(10^x), or f2(x) = e^(-2*x). Note that the latter still fits the format, with b = e^(-2). The inverse is the logarithmic function. So for y = f1(x) = 3*(10^x), reverse the x & y, and solve for y:x = 3*(10^y)log(x) = log(3*(10^y)) = log(3) + log(10^y) = log(3) + y*log(10) = y*1 + log(3)y = log(x) - log(3) = log(x/3)The second function: y = e^(-2*x), the inverse is: x = e^(-2*y).ln(x) = ln(e^(-2*y)) = -2*y*ln(e) = -2*y*1y = -ln(x)/2 = ln(x^(-1/2))See related link for an example graph.
y = ln (x) dy/dx = 1/x
y=logx y=10 logx= 10 10logx = 10log1 logx = log1 x = 1 //NajN
For a quotient x/y , then its log is logx - log y . NOT log(x/y)
1
log(1) = 0log(x*y) = log(x) + log(y)If logb(x) = y then x = by.
Not quite. The log(x/y) = log(x) - log(y) In words, this reads "The log of a quotient is the difference of the log of the numerator and the log of the denominator."
log of the square root of 'y' = 1/2 sqrt(y)
Here are a few, note x>0 and y>0 and a&b not = 1 * log (xy) = log(x) + log(y) * log(x/y) = log(x) - log(y) * loga(x) = logb(x)*loga(b) * logb(bn) = n * log(xa) = a*log(x) * logb(b) = 1 * logb(1) = 0
y = 10 y = log x (the base of the log is 10, common logarithm) 10 = log x so that, 10^10 = x 10,000,000,000 = x
Sometimes you need to take logs, or antilogs, on both sides of an equation. Sometimes you need to apply certain common logarithmic identities, especially: log(xy) = log x + log y log (x/y) = log x - log y log (ab) = b log a
The word "psychology" consists of three morphemes: "psycho" (meaning mind or mental), "log" (meaning study or science), and "y" (a suffix indicating a field of study). Each morpheme carries its own meaning and contributes to the overall meaning of the word "psychology."
log base m of x = y is equivalent to x=m^y
Log(y) can be any number, positive or negative, no limits. It all depends on the value of 'y'.
let x and y be two numbers ex = y log y = x antilog x = y