1. a) use properties of logarithmic to condence he logarithmic expression below. write the
expression as a single logarithmic whose coefficient in 1
log y +2 logz (since m log a= log a^m)
=log y + logz^2 (since log m+ lg n =log mn)
=log yz^2
b) Use properties of logarithmic to expand logarithmic expression as possible.
log base b(y^2x)
log base b y^2 +log base b x
2log base b y +log base b x
c) solve logarithmic equation. be sure to reject any values of x that is not in the domain of the
original expression . Give exact answer.
log m -log n =log m/n
ln(x-2)/(x+6)=ln(x-1)/(x+12)
(x-2)/(x+6)=(x-1)/(x+12)
(x-2)*(x+12)=(x+6)(x-1)
x^2 +10x -24 =x^2 +5x -6
5x=18
x=18/5
d)find f(g(x)) and g(f(x)) and determine whether the pair of functions fand g are inverses of each
other
f(x)=4x and g(x)=4x
so f(g(x))=4(4x)=16x
so g(f(x))=4(4x)=16x
e)solve the exponetial equation. express the solution in natural logarithmic. than obtain decimal.
5^(x+2)=401
x+2=log base5 401
x=-2+log base5 401
x=-2 +(ln 401)/(ln 5)
x=1.72
Solution
a) use properties of logarithmic to condence he logarithmic expression below. write the
expression as a single logarithmic whose coefficient in 1
log y +2 logz (since m log a= log a^m)

2. =log y + logz^2 (since log m+ lg n =log mn)
=log yz^2
b) Use properties of logarithmic to expand logarithmic expression as possible.
log base b(y^2x)
log base b y^2 +log base b x
2log base b y +log base b x
c) solve logarithmic equation. be sure to reject any values of x that is not in the domain of the
original expression . Give exact answer.
log m -log n =log m/n
ln(x-2)/(x+6)=ln(x-1)/(x+12)
(x-2)/(x+6)=(x-1)/(x+12)
(x-2)*(x+12)=(x+6)(x-1)
x^2 +10x -24 =x^2 +5x -6
5x=18
x=18/5
d)find f(g(x)) and g(f(x)) and determine whether the pair of functions fand g are inverses of each
other
f(x)=4x and g(x)=4x
so f(g(x))=4(4x)=16x
so g(f(x))=4(4x)=16x
e)solve the exponetial equation. express the solution in natural logarithmic. than obtain decimal.
5^(x+2)=401
x+2=log base5 401
x=-2+log base5 401
x=-2 +(ln 401)/(ln 5)
x=1.72