Regents Exam Questions A2.A.27, 28 : Exponential Equations
Page 1
2014
A2.A.27: Exponential Equations: Solve exponential equations with and without
common bases
A2.A.28: Logarithmic Equations: Solve a logarithmic equation by rewriting as an
exponential equation
Part I
3 Solve algebraically for x:
4 Solve algebraically for x:
5 Solve for x:
16 Solve for x:
Part II
16 What is the value of x in the equation
expressed to the nearest hundredth?
3 Using logarithms, solve the equation
for x to the nearest integer.
17 Given:
Find x, to the nearest tenth, when
4 Using logarithms, solve the equation
to the nearest tenth.
5 Using logarithms, solve the equation
to the nearest tenth.
,
.
for x
for x
18 Using logarithms, solve for x to the nearest
hundredth:
Part III
6 Solve for x:
11 Solve for x to the nearest hundredth:
3 Solve for x:
12 Solve for x to the nearest hundredth:
4 Solve for x:
14 Using logarithms, find w to the nearest hundredth:
5 Solve for all values of x:
7 Solve for x:
Regents Exam Questions A2.A.27, 28 : Exponential Equations
Page 2
2014
8 Solve algebraically for all values of x:
Part IV
1 If
, then x is equal to
2 What is the solution of the equation
?
8 If
, find the value of x.
9 If
, find x.
10 If
, find x.
11 If
and
numerical value of
3 If
, find the value of x.
4 Solve for x:
5 Find x if
.
6 Solve algebraically for x:
7 If
, what is the value of x?
, find the
, in simplest form.
12 The temperature, T, of a given cup of hot
chocolate after it has been cooling for t minutes
can best be modeled by the function below,
where is the temperature of the room and k
is a constant.
A cup of hot chocolate is placed in a room that
has a temperature of 68°. After 3 minutes, the
temperature of the hot chocolate is 150°.
Compute the value of k to the nearest
thousandth. [Only an algebraic solution can
receive full credit.] Using this value of k, find
the temperature, T, of this cup of hot chocolate
if it has been sitting in this room for a total of
10 minutes. Express your answer to the
nearest degree. [Only an algebraic solution
can receive full credit.]
Regents Exam Questions A2.A.27: Exponential Equations 5
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