Log Base 32768 of 2

What is Log Base 32768 of 2 or log32768(2)?


Log32768(2)

= 0.066666666666667

Formula How to

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How to find what is Log Base 32768 of 2? The logarithm of a number to a given base is the exponent to which the base must be raised to produce the number. In mathematical terms, if "b" is the base and "x" is the number, then the logarithm of "x" to the base "b" is written as logb(x) and is defined as the exponent "y" such that b^y = x.

The logarithm of a number to a given base is a useful tool in many areas of mathematics and science, including finance, engineering, and physics. It's also used in solving exponential equations and in graphing logarithmic functions.

In mathematics, the most common logarithms are logarithms to the base 10, which are called common logarithms, and logarithms to the base e, which are called natural logarithms. The natural logarithm is denoted by the symbol ln, and has special properties in calculus and other areas of mathematics.

To calculate any "log base of" use this fromula, which is given below-

logb(x) =
loge(x)/loge(b)
; x>0, b>1;

Where,

  • b = base;
  • x = value;

For calculation, here's how to calculate log base 32768 of 2 using the formula above, step by step instructions are given below

  1. Input the value as per formula.
    log32768(2) =
    loge(2)/loge(32768)
  2. Calculate the log value for numerator and denominator part.
    0.69314718055995/10.397207708399
  3. After simplify the fraction, you will get the result. Which is,
    0.066666666666667

log32768(2) or Log Base 32768 of 2 is equal to 0.066666666666667.

loge(32768) 10.397207708399
log10(32768) 4.5154499349597

loge(2) 0.69314718055995
log10(2) 0.30102999566398

logb(x) Equal to
log32768(1) 0
log32768(2) 0.066666666666667
log32768(3) 0.10566416671474
log32768(4) 0.13333333333333
log32768(5) 0.15479520632582
log32768(6) 0.17233083338141
log32768(7) 0.18715699480384