three laws of logarithms

The sum of the infinite series 1 + 1/1! + 1/2! + 1/3! + 1/4! + ... is called the exponential number. If x is any complex number then the series is called the exponential series. It can be proved mathematically that this exponential series has a sum and we denote it by e x ..

We know that log 2 8 is the number to which 2 must be raised to get 8. Therefore, log 2 8 = 3. In general, if a x = y, (a > 0), then we say that log a y = x. If e x = y, then we say that the natural logarithm of y is x and we write log y = x. In other words, if the base of a ..

2 < e < 3 The value of e rounded off to four decimal places is 2.7183. For complex numbers x,y, we have e x + y = e x y y . For any rational number x, the sum, e x , of the series ..

The volume of a given mass of a dry gas is inversely proportional to its pressure, temperature remaining constant. Robert Boyle (1627 - 1691) discovered this law in 1662 and it was named after him. It can be restated as "The product of the volume and pressure of a given mass of dry gas is..

Identify the basic logarithmic function from the graphs. => Graph 5 or Graph 3 or Graph 1 or Graph 2 or Graph 4..

Johannes Kepler derived three laws, which govern the planetary motion. These are, 1. The orbit of a planet is an ellipse with the Sun at the one of the foci. 2. The line joining the planet and the Sun sweeps equal areas in equal intervals of time. 3. The cube of the mean distan..

Avogadro's Law - The relationship between the volume of a gas to the number of molecules at constant temperature and pressure is known as Avogadro's law. It states that equal volumes of all gases under similar conditions of temperature and pressure contain equal number of molecu..

. Fig: 2.3 - Plot of P versus 1/V The P-V curve for a given gas is different at different temperatures. The plot of 'PV' against 'P' at different temperature is known as Isotherms. The higher curve corresponds to higher temperature. Boyle's law expresses the compressible nature ..

. Thermal equilibrium now demands that E = a I ....................... (2) Where E is the radiant energy per unit time per unit area emitted by the (non-black) body. It follows from Eq.(1) that ....................... (3) But in terms of emissivity e already defined ........................

Use the laws of logarithms to rewrite the following. log 5 39 9 => log 9 39 - log 5 39 or 9 log 5 39 or log 5 39 + log 9 39 or 5 + log 9 39..