Solve each equation. Give the exact solution. See Example 3.
33.Concept Check Suppose that in solving a logarithmic equation having the term
, you obtain a proposed solution of 2. All algebraic work is correct. Why must
you reject 2 as a solution of the equation?
34.Concept Check Suppose that in solving a logarithmic equation having the term
, you obtain a proposed solution of All algebraic work is correct. Should
you reject as a solution of the equation? Why or why not?
Solve each equation. Give exact solutions. See Examples 4 and 5.
Solve each problem. See Examples 6 – 8.
- (a)How much money will there be in an account at the end of 6 yr if $2000 is deposited
at 4% compounded quarterly? (Assume no withdrawals are made.)
(b)To one decimal place, how long will it take for the account to grow to $3000?
- (a)How much money will there be in an account at the end of 7 yr if $3000 is deposited
at 3.5% compounded quarterly? (Assume no withdrawals are made.)
(b)To one decimal place, when will the account grow to $5000?
- (a)What will be the amount Ain an account with initial principal $4000 if interest is
compounded continuously at an annual rate of 3.5% for 6 yr?
(b) To one decimal place, how long will it take for the initial amount to double?
50.Refer to Exercise 48(a).Does the money grow to a greater value under those conditions,
or when invested for 7 yr at 3% compounded continuously?
51.Find the amount of money in an account after 12 yr if $5000 is deposited at 7% annual
interest compounded as follows.
(a)Annually (b) Semiannually (c)Quarterly
(d)Daily (Use .) (e)Continuously
52.How much money will be in an account at the end of 8 yr if $4500 is deposited at 6%
annual interest compounded as follows?
(a)Annually (b) Semiannually (c)Quarterly
(d)Daily (Use .) (e)Continuously
53.How much money must be deposited today to amount to $1850 in 40 yr at 6.5% com-
pounded continuously?
54.How much money must be deposited today to amount to $1000 in 10 yr at 5% com-
pounded continuously?
n= 365
n= 365
log 2 x+log 2 1 x- 62 = 4 log 2 x+log 2 1 x+ 42 = 5
log 5x-log 12 x- 12 =log 4 log 3 x+log 3 12 x+ 52 = 1
log 2 x+log 2 1 x- 72 = 3 log 12 x- 12 +log 10x=log 10
log 4x-log 1 x- 32 =log 2 log 1 - x 2 +log 3=log 12 x- 152
log 5 13 t+ 22 - log 5 t=log 5 4 log 2 1 x+ 52 - log 2 1 x- 12 =log 2 3
log 16 x+ 12 =log 3 log 17 - 2 x 2 =log 4
- 4
log 13 - x 2 - 4.
log 1 x- 32
log 7 1 x+ 123 = 2 log 4 1 x- 323 = 4
log 2 12 x- 12 = 5 log 6 14 x+ 22 = 2
log 3 16 x+ 52 = 2 log 5 112 x- 82 = 3
620 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions
