Algebra 2
Review for Test on Unit 10
Name:
1) Which expression is not equivalent to logb 36 ?
(1) 6 logb 2
(3) 2 logb 6
(2) logb 9  logb 4
(4) logb 72  logb 2
2) The function y  2 x is equivalent to
(1) x  y log 2
(3) y  x log 2
(2) x  log 2 y
(4) y  log 2 x
3) In the equation log x 4  log x 9  2, x is equal to
(1) 13
(2) 6
(3) 6.5
(4) 18
4) Which value makes y = log2x undefined?
1
(1) 3
(3)
2
(2) -5
(4) π
1
5) The expression 2 log x  log y is equivalent to:
3
(1) log
6) If d 
x
y
3
(2) log
x2
3 y
(3) log 3 xy
ab 2
, then log d is equal to:
c2
1
(1) log a  (log b  log c)
2
(3) log a  2(log b  log c)
(2) log a  log b  log c
1
1
(4) log a  log b  log c
2
2
(4) log( x  y3 )
7) Solve for x:
8) Solve for x:
9) Find x using your calculator.
Round to the nearest thousandth:
10) When Alex was born, his parents
invested $4000 in a savings
account that paid 5% compounded
continuously. What is the value of
the account after 17 years to the
nearest dollar? {Use
}
11) Verify the following by evaluating the
logarithms:
12) Use properties of logarithms to
show that:
( )
13) Solve for x:
((
) )
14) Use the change of base rule to solve
for x:
(
)
(
)
16) Solve for x to the nearest hundredth:
15)
2
Solve for x: log x 1 ( x  7)  log x 1 2  2
17) Solve for x rounding to four decimal places:
18) The population of a town is represented by
the formula P(t )  A(1.2) t where A is the
current population and t is time. Determine,
to the nearest tenth of a year, how long it
would take the population to reach 5000
people if the current population is 3750.
19) Solve for x to the nearest tenth:
20) Given:
in terms of
, express
√
21) Use the approximate logarithm values below to estimate the value of each of the following
logarithms.
( )
( )
( )
a)
(
)
b)
22) Write each expression in terms of A and B if log 2 x  A and log 2 y  B .
( )
a)
( )
b)
23) Given:
a)
and
, find:
b)
√
24) Use the change of base rule and the properties of logarithms to show that each of the
following expressions is equivalent to a rational number.
a)
b)
( )
25) Solve for x:
(
)
(
26) Solve the following equation:
)
(
(
)
)
(
)