1.) Use the product or quotient rule for logarithms to find allxvalues such that log₄(3x- 2) + log₄(x+ 22) - log₄(x+ 1) = 3.

2.) Atmospheric pressurePin pounds per square inch is represented by the formulaP= 14.7e^-0.21x, wherexis the number of miles above sea level. To the nearest foot, how high is the peak of a mountain with an atmospheric pressure of 5.728 pounds per square inch?

NOTE: there are 5,280 feet in a mile

3.) Newton's Law of Cooling states that the temperature(T) of an object at any time (t), in minutes, can be described by the equationT=T_S+ (T₀-T_S)e^-kt, whereT_Sis the temperature of the surrounding environment,T₀is the initial temperature of the object, andkis the cooling rate.

What is the cooling rate of an object if the initial temperature was 400 C, the surrounding environment temperature was 30 C, and it took 105 minutes to cool down to 125 C. Round your result to 3 decimal places.

4.) Mercury 197 has a decay rate of 1.066% per hour. Given the exponential model representing the amount of Mercury 197 remaining afterthours, find how long it will take387 grams of the Mercury 197 to decay to 38 grams. Round your result to the nearest thousandth hour.

A(t) =A₀e^ln(0.98934)t

5.) Solve each system by any method.

9x+ 8y= 0 and 6x- 12y= -13

6.) A moving company charges a flat rate of $650, and an additional $4.95 for each box. If an Uber service would charge $35 for each box, how many boxes would you need for it to be cheaper to use the moving company, and what would be the total cost?

Please show the work for how you arrived at these solutions. Thank you!