# Using Logarithms

Part1:

Using the library,web resourses,and other materials, find the hydrogen ion concentration,[H+], of the substance using the formula. Discuss the meaning of pH and [H+], the pH scale and why your chosen substance is acidic. Use scientific notion or enough decimal places so that your answer has at least 3 place values. For example, either use 3.44*10^-6 or 0.00000344.

Be sure to reference your resources using APA style.

Part2:

Suppose that the number of cars, C, on 1st Avenue in a city over a period of time t, in months, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the nuber of cars driven on 1st Avenue can be modeled by an exponential function, C=p*a^t. Where p is the number of cars on the road on the first day recorded. If you commuted to work each day along 1st Avenue, would you perfer that the value of "a" be between 0 and1 or larger than 1? Explain your reasoning.

Be sure to reference your sources using APA style.

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#### Solution Preview

Part 1:

You haven't given me a substance to work with, but as an example you could use a acetic acid solution with a PH of 4.6 (workings below)

The best way to work out the concentration of [H+] is from the pH of a solution.

If you measure the pH of a given solution, concentration of H+ is calculated applying the definition:

pH = - log [H+] (logarithm in base 10)

so, [H+] = 10^-pH

For example, if an acetic acid solution has a pH= 4.6 then the [H+] = 10^-4.6 = 2.51 x 10^-5 mol/L

(If you have a given substance that you forgot to post just sub the negative ...

#### Solution Summary

Logarithms and their characteristics

Problems invloving logarithms

Compounded Annuity Solving for Rate using Logarithms

If it takes 9 years for a one-time deposit in a savings account that receives interest compounded quarterly to triple, then what is the interest rate to the nearest tenth of a percent?

To answer this question, you will need to utilize the following relationship:

If ln(x) = N, where N is some number, then x = eN

(if using logarithms to the base 10, then equivalently,

If log(x) = N, then x = 10N )

Please show formula and steps.

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