 # Logarithm: senior math exercises corrected in PDF.

Logarithms with corrected senior math exercises involve several interesting properties as well as functions.

These corrected exercises on logarithms involve the following concepts:

1. definition of the logarithm;
2. functional equations;
3. algebraic formulas on logarithms;
4. limits and logarithm functions.

Exercise #1:

Solve the following equations: Exercise #2:

Solve the following equations: Exercise #3:

Simplify the writing of the following numbers: Exercise #4:

After having specified the set of definition of the solutions of the equation, solve it. Exercise #5:
Let f be the function defined on by: .
We note its graphic representation in an orthonormal reference frame of the plane (graphic unit: 2 cm).
1. Study the limit of f at 0. Interpret this result graphically.
2. a. Study the limit of f in .
b. Show that the line with equation is an asymptote to in .
Study the position of in relation to .
3. Study the variations of f. Draw up its table of variations.
4. Prove that the equation f(x) = 0 has a unique solution in the interval and determine a frame of of magnitude .
5. Draw the line and the curve .

Exercise #6:

Also useful for the baccalaureate… in Chemistry!
In chemistry, we know that the pH of a solution allows us to express its acidic or basic character.
This number is a decimal between 1 and 14 so that :
● If pH < 7, then the solution is said to be acidic.
● If pH > 7, then the solution is said to be basic.
● If pH = 7, it is said to be neutral. It is then known that the pH is associated with the relation where is the concentration of ions , expressed in mol/L.

1. A solution has a concentration of ions equal to .
What is its pH? What can we say about a solution whose ion concentration is ?
equal to 0.1 ?
2. What is the ion concentration of a neutral solution?
3. If you increase the concentration of ions in a solution, do you decrease or increase the pH of the solution?
4. What must be done to a solution to increment or decrement its pH?

Vocabulary : To increment is to add 1. So decrementing is… ?

Exercise #7:
f is the function defined on by : .
C is its curve in an orthogonal reference frame .

1. a. Determine the limit of in .
b. Deduce the existence of an oblique asymptote of which we will specify an equation.
c. Show that for any real x : d. Determine the limit of f at , and the existence of a second oblique asymptote .
2. Show that the y-axis is an axis of symmetry for C.
3. Solve the inequation .
4. Study the variations of the function f.
5. Show , and C, after indicating the position of and C.

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