Differential calculus
Ida Karimfazli
MATH104-106
Fall 2015
Week 0 - examples on logarithms
Sept. 10, 2015
Example 1.
Solve the following equations
a. 9x
2 −3x+3/2
= 1/3
2 −3x+3/2
9x
x2 −3x+3/2
log9 9
=
1
3
1
= log9
3
log3 (1/3)
=
log3 9
log3 1 − log3 3
=
log3 32
0−1
=
2
3
2
3
x2 − 3x +
2
3
x2 − 3x +
2
3
1
x2 − 3x + + = 0
2 2
x2 − 3x + 2 = 0
(x − 2)(x − 1) = 0
x = 2, 1
x2 − 3x +
b. 2log3 (x+2) = 5
2log3 (x+2) = 5
log2 2log3 (x+2) = log2 5
log3 (x + 2) = log2 5
3log3 (x+2) = 3log2 5
x + 2 = 3log2 5
x = 3log2 5 − 2
1
Differential calculus
Ida Karimfazli
MATH104-106
Fall 2015
Example 2.
In the following equation, make y the subject: logy 3 = x2 − 2x
logy 3 = x2 − 2x
log3 3
= x2 − 2x
log3 y
1
log3 y = 2
x − 2x
2
y = 31/(x −2x)
2