Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Problem
Problem
Calculate the value of each of the following logarithms: It is given that
log
a
b
a
=
3
\log_{ab} a = 3
lo
g
ab
a
=
3
, where
a
,
b
∈
R
+
a, b \in \mathbb{R}^+
a
,
b
∈
R
+
,
a
b
≠
1
ab \neq 1
ab
=
1
. a.
log
2
1
16
\log_2 \frac{1}{16}
lo
g
2
16
1
. b.
log
9
3
\log_9 3
lo
g
9
3
. c.
log
3
81
\log_{\sqrt{3}} 81
lo
g
3
81
. d. Show that
log
a
b
b
=
−
2
\log_{ab} b = -2
lo
g
ab
b
=
−
2
. e. Hence find the value of
log
a
b
a
3
b
\log_{ab} \frac{\sqrt[3]{a}}{\sqrt{b}}
lo
g
ab
b
3
a
.
Browse the problem library