Mathedu Courses
Mathedu Courses
Lecture 0 - HW & SW requirements public
Lecture 1 - Introduction public
Lecture 2 - Arithmetic operations public
Lecture 3 - Trigonometric functions public
Lecture 4 - Exponent related functions public
Test Section 2 public
Lecture 5 - Conditionals if elif else public
Lecture 6 - Sequential loops for public
Test Section 3 public
Lecture 9 - Conclusion public
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Lecture 0 - HW & SW requirements public
Lecture 1 - Introduction public
Lecture 2 - Arithmetic operations public
Lecture 3 - Trigonometric functions public
Lecture 4 - Exponent related functions public
Test Section 2 public
Lecture 5 - Conditionals if elif else public
Lecture 6 - Sequential loops for public
Test Section 3 public
Lecture 9 - Conclusion public
First published on Sunday, Feb 22, 2026 and last modified on Sunday, Feb 22, 2026
Fabienne Chaplais Email
Exponent Related Functions
Now let's see the exponent related functions, with numpy package.
First let's see the natural logarithm and the exponential.
The function log of numpy package is the natural logarithm.
log of 1 is 0 and log of e is 1.
e is the number exponential of 1.
The function exp is the exponential.
exp of 0 is 1, exp of 1 is the number e by definition of e, exp of -1 is 1 over e.
The functions exp and log are mutually reciprocal.
For x positive, exp of log of x is x.
For any real number y, log of x of y is y.
But let's see it in practice.
Launch Anaconda in Spyder and follow me.
First we type 'from numpy import *', in order to have the functions available and the number e.
from numpy import *log of 1 is 0.
log(1)And log of 0? It is minus infinity and we have an error.
log(0)log of 10 is not at all 1.
log(10)But log of the number e, that is given in NumPy, is 1.
log(e)The exponential now.
exp of zero is one.
exp(0)exp of one is so.
exp(1)Is it equal to, equal equal, e? Yes, it's true.
exp(1)==eexp of minus one.
It is so.
exp(-1)Is it equal to one over e? Yes, it's true.
exp(-1)==1/eAnd now exp of log of 3.5.
It is 3.5, it is the same.
exp(log(3.5))And log of exp of a negative number, let's say, minus 3.2.
It is minus 3.2, it is also the same.
log(exp(-3.2))Now let's see the decimal logarithm and powers of 10, the generalized powers of 10.
The function log10 is the decimal logarithm.
Log10 of 1 is 0 and log10 of 10 is 1.
It is the usual logarithm.
The function 10**x is 10 to the power x.
10 to the power 0 is 1, 10 to the power 1 is 10, 10 to the power -1 is 0.1.
And 10 to the power 1/2? is the square root of 10.
The functions power of 10 and log10 are mutually reciprocal.
For x positive, 10 to the power log10 of x is x.
And for any y real number, log10 of 10 to the power y is y.
But let's see it in practice.
Launch and Aconda and Spider and follow me.
First we type from numpy import *.
from numpy import *Log10, the decimal logarithm, of 1 is 0.
log10(1)Log10 of 0, there is an error, it's t is minus infinity.
log10(0)Log10 of 10, the decimal logarithm of 10, is 1. That's why it's called the decimal logarithm.
log10(10)log10 of 100 is 2, because 100 is 10 to the power 2.
log10(100)10 to the power 0 is 1.
10**010 to the power 1 is 10.
10**110 to the power -1 is 0.1.
10**(-1)And 10 to the power 3 is 1,000.
10**310 to the power minus 2 is 0.01.
10**(-2)And 10 to the power one half is so.
10**(1/2)Is it equal to sqrt, the square root, (the square root is also given in numpy) the square root of 10? Yes it's true.
10**(1/2)==sqrt(10)10 to the power decimal logarithm of 5.25.
It is 5.25.
10**(log10(5.25))And log10 of 10 to the power, decimal logarithm of 10 to the power 0.3.
It is 0.3.
log10(10**0.3)What's coming now? What's coming now is the control flows, the conditional if elif else, and the loops for.