Common Mathematical Functions (1.4.2)

Question 1

• The equation for a line and the quadratic equation are useful in chemistry.

Answer 1

• The equation for a line and the quadratic equation are useful in chemistry.

Question 2

• Logarithms are useful for collapsing measurements that are on an extremely large or small scale into a more manageable scale.

Answer 2

• Logarithms are useful for collapsing measurements that are on an extremely large or small scale into a more manageable scale.

Question 3

The equation for a line and the quadratic equation
are useful in chemistry.

The equation for a line is y = mx + b. In this
equation, m is the slope of the line and b is the yintercept. The slope is rise over run. In the
example to the left, rise (the change in y) is 0.8 over
a run (change in x) of 2.0, so the slope is 0.8/2.0 or
0.4. The y-intercept is the value of y when x equals
zero. In the example to the left, the y-intercept is
1.2.

The quadratic equation is y = ax^2 + bx + c. The
graph shown is for the quadratic equation
y = x^2 + 2x – 3. The points where the parabola
described by a quadratic equation crosses the xaxis
can be found using the quadratic formula.
Since the quadratic formula includes both a positive
and negative root, it will always have two solutions.
However, in general only one of the solutions will
have a meaning in chemistry.

Answer 3

The equation for a line and the quadratic equation
are useful in chemistry.

The equation for a line is y = mx + b. In this
equation, m is the slope of the line and b is the yintercept. The slope is rise over run. In the
example to the left, rise (the change in y) is 0.8 over
a run (change in x) of 2.0, so the slope is 0.8/2.0 or
0.4. The y-intercept is the value of y when x equals
zero. In the example to the left, the y-intercept is
1.2.

The quadratic equation is y = ax^2 + bx + c. The
graph shown is for the quadratic equation
y = x^2 + 2x – 3. The points where the parabola
described by a quadratic equation crosses the xaxis
can be found using the quadratic formula.
Since the quadratic formula includes both a positive
and negative root, it will always have two solutions.
However, in general only one of the solutions will
have a meaning in chemistry.

Question 4

Logarithms are useful for collapsing measurements
that are on an extremely large or small scale into a
more manageable scale.

A logarithm is the power to which a base must be
raised to obtain a given result. For example, if
10^x = a, x is the base-10 logarithm of a. The base-
10 logarithm is written log10.

Another type of logarithm is the natural logarithm,
abbreviated ln. The natural logarithm is the base-e
logarithm, where e = 2.718281829… The natural
logarithm appears in many natural relationships.

Answer 4

Logarithms are useful for collapsing measurements
that are on an extremely large or small scale into a
more manageable scale.

A logarithm is the power to which a base must be
raised to obtain a given result. For example, if
10^x = a, x is the base-10 logarithm of a. The base-
10 logarithm is written log10.

Another type of logarithm is the natural logarithm,
abbreviated ln. The natural logarithm is the base-e
logarithm, where e = 2.718281829… The natural
logarithm appears in many natural relationships.