PLEASE ANSWER ALL OF THE QUESTIONS ON THE PICTURE, PLEASE. MISTERAVUST. TELUTUI LvyumurinneSummaryA useful method to express a number is in logarithmic format. A logarithm is the exponent that a base must be raised to produce a given number.Mathematically, if base* = y then logbase (y) = x. For example we know that 10² = 100 then the log₁0 (100) = 2. Likewise since 10-²0.01 thenlog₁0 (0.01) = −2. Commonly for a base of 10 the logarithm symbol log is used. Thus for 104 = 10,000 the log₁0 (10,000) = 4.Logarithms are not confined to base 10. For 3² = 9 then log3 (9) = 2. A commonly used scientific base is Euler's number, 2.71828... Logarithms based uponEuler's number are called natural logarithms having the symbol In. Scientific calculators readily calculate both the log and In of numbers.Antilogarithms are the inverse function of a logarithm. If logbase (x) = y then the antilogbase (y) = x. In other words base = x. The antilog(2) = 100.Antilog(-2) = 0.01. Like wise there are antilogarithms for natural logarithms. To determine the antilogartihm of a natural logarithm employ the e* functionon your calculator.Math ExampleCalculate In(74.10).In(74.10) =€7.98Calculate e€7.98Chemistry ExampleA freshly purified 1.8000 g sample of pure 32P decays for 7.000 days. After that time the remaining amount of 32P has a mass of 1.2819 g. What is the decay(rate) constant, in day¯¹, for the radioactive decay of 32 P?-1Rate constant =CheckA freshly purified 2.780 g sample of pure0.2661 year¯¹.-1day ¹g22 Na is22 Na is made in the lab. How many grams of 22 Na remain after 1.150 years? The decay (rate) constant forPreviousNext

ln(74.10) = 4.31 e7.98=2.92×103We know that All the radio active substances undergo first order kinetics For the first order reaction, k=1tlnN0Nwherek=rate constantt = time takenN0=initial concentration (amount)N=conc. after time tinitial amount of 32P = N0 = 1.8000 gtime = 7 days amount of P after that time = 1.2819 g We know that k=1tlnN0Nk=17.000 daysln1.80001.2819k=17.000 days×0.339443k=0.048492 day-1