Given that log8,(x + 2) + log8, y =z-1/3 and that log2, (x - 2) - log2, y = (2z + 1) show
that x= 32^z + 4. If z = 1, find the numerical values of x and y.
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2
Answer:
Rewrite as an equation.
log
2
(
32
)
=
x
Rewrite
log
2
(
32
)
=
x
in exponential form using the definition of a logarithm. If
x
and
b
are positive real numbers and
b
does not equal
1
, then
log
b
(
x
)
=
y
is equivalent to
b
y
=
x
.
2
x
=
32
Create equivalent expressions in the equation that all have equal bases.
2
x
=
2
5
Since the bases are the same, the two expressions are only equal if the exponents are also equal.
x
=
5
The variable
x
is equal to
5
.
5
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