...of a right-angled triangle, in which the perpendicular is 127 and the hypotenuse 325. 9. Prove that the logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers themselves. Find A, when 10 tan A = 7 sin 15° 30'. 10. In the triangle...

...always positive and not equal to one. 4.2. Laws of logarithm (i) logu (mx /i) = logam + log,/! ie, the logarithm of the product of two numbers is equal to the sum of their logarithms. Proof : Let logam = x and loga/i = у :. a? = m ... (1) and a? = n ... (2). Multiplying...

...substitute for the term "index", the laws of logarithms can be easily deduced from the laws of indices. /. Logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers to quantities, Le.. Proof. Let loga m = x so that of = m ...(I) and loga...