Exam 5: Exponential-And-Logarithmic-Functions

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) ​ Log 5x⁴y ​

Let Q represent a mass of radioactive plutonium (in grams), whose half life is 24,100 years.The quantity of plutonium present after t years is .Determine the quantity present after 67,000 years.Round your answer to one decimal place. ​

Write the logarithmic equation in exponential form. ​ ​

Rewrite the logarithm as a ratio of natural logarithms. ​ Log_1/5 x ​

$3000 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places.) ​ ​

The population P of a culture of bacteria is described by the equation , where t is the time, in hours, relative to the time at which the population was 1300.What was the population at hours? ​

Use a graphing utility to determine which graph below is the graph of the function. ​ ​ ​

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms.(Assume all variables are positive.) ​ Log₃ 9x ​

Evaluate the logarithm using the change-of-base formula.Round your result to three decimal places. ​ Log₂ 7 ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​ ​

If $1 is invested in an account over a 10-year period, the amount in the account, where t represents the time in years, is given by depending on whether the account pays simple interest at or continuous compound interest at 7%.Graph each function on the same set of axes.Which grows at a higher rate? ​

Identify the value of the function at .Round to 3 decimal places.

Determine whether or not is a solution to .

Select the graph of the exponential function. ​ ​

Rewrite the logarithm as a ratio of natural logarithms. ​ Log_3.1 x ​

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​ Function Value ​

Write the exponential equation in logarithmic form. ​ ​

Evaluate the function at the indicated value of x.Round your result to three decimal places. ​ Function Value ​

Solve the equation for x using the One-to-One Property.

Select the graph of the function. ​ ​