16) Use the Laws of Logarithms to combine the expression.

4 log(x) ? 1/3 log(x² + 1) + 3 log(x ? 1)

18) Find the domain of the function. (Enter your answer using interval notation.)

g(x) = log₄(x² ? 9)

23) Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals.

f(x) =7^x?1

f(1/2)=

f ( 1.5) =

f( -1)=

f ( 1/4)=

24) Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model:

P(t) = d

d over

1 + ke^?ct

where c, d, and k are positive constants. For a certain fish population in a small pond d = 1400, k = 13, c = 0.2, and t is measured in years. The fish were introduced into the pond at time t = 0.(a) How many fish were originally put in the pond? fish (b) Find the population after 10, 20, and 30 years. (Round your answers to the nearest whole number.)

10 years	fish
20 years	fish
30 years	fish

(c) Evaluate P(t) for large values of t. What value does the population approach as t??? P(t) = Does the graph shown confirm your calculations?

28) Use the Laws of Logarithms to expand the expression.

log₈(x square root y)

30) Consider the following.

10^x=121

(a) Find the exact solution of the exponential equation in terms of logarithms.

x= l

31) In the formula

A(t) = Pe^rt

for continuously compound interest, the letters P, r, and t stand for ---Select--- number of years amount after t years prime rate percent interest principal , ---Select--- investment per year interest rate per day investment amount rate of return interest rate per year , and ---Select--- number of days number of times interest is compounded per year number of years number of months number of time periods , respectively, and A(t) stands for ---Select--- amount after t days amount after t years amount of principal amount of interest earned in year t amount of interest earned after t years . So if $300 is invested at an interest rate of 6% compounded continuously, then the amount after 5 years is $ . (Round your answer to the nearest cent.)

32) Consider the following.

10^?x = 4

(a) Find the exact solution of the exponential equation in terms of logarithms.

x =

34) Consider the following.6^x/14 = 0.1(a) Find the exact solution of the exponential equation in terms of logarithms.

x = (b) Use a calculator to find an approximation to the solution rounded to six decimal places.

x =

34.) x = 14 log o's Can be also written as- JC = 14 log to 6 Q ) = ) = - 14 log 10 b . ) = ) x = - 17 . 9913 6093 W - 17 . 991361 32 - ) - x - 121 10 Taking bog both the side , base =so -) Dog 10"= 109 121 10 = ) - x Dog 10 = log 121 = ) - xc = jag 10 D = - log 121 LO Can be written as ; x = - log (1 1)2 10 X = - 2. 082785 xc = - 2 log 1 1