What Is the Discrete Logarithm of 100000000 in Base 10?

[bmorgan]

How to solve log100000000, base is 10.

 

[chiro]

How to solve log22 for the prime p = 47, base is 10. I can convert this to 10^x = 22(mod 47). How to solve this problem?

Hey bmorgan and welcome to the forums.

Are you aware of Fermats theorem and Eulers theorem for exponent problems?

Also are you doing this as part of structured coursework/research or as something akin to self-study?

 

[HallsofIvy]

Boy, am I confused!
bmorgan appears to have written

How to solve log100000000, base is 10.

but chiro quotes

How to solve log22 for the prime p = 47, base is 10. I can convert this to 10^x = 22(mod 47). How to solve this problem?

I really wish people would not edit quite so heavily!

But the original problem posted is certainly non-trivial while the new one is, to put it simply, trivial- at least to anyone who would be expected to solve the first problem.

bmorgan, do you know what "logarithm base 10" means?

100000000 equals 10 to what power?

 

[chiro]

Naughty boy mr bmorgan!

 

[CellCoree]

To solve this discrete logarithm, we need to find the exponent that when raised to the base 10, gives us 100000000. This can be done by using the basic definition of logarithms, which states that log base a of b is equal to c if and only if a^c = b.

In this case, we need to find c, which is the exponent, such that 10^c = 100000000. We can use the property of logarithms that states that log base a of a^c is equal to c. Therefore, we can rewrite the equation as log base 10 of 10^c = c.

Now, we know that 10^8 = 100000000, so the solution to this logarithm is 8. Therefore, log100000000, base 10 is equal to 8. We can also verify this by plugging in the values into a calculator and seeing that 10^8 does indeed equal 100000000.

In summary, to solve a discrete logarithm, we need to find the exponent that when raised to the base, gives us the desired value. This can be done by using the basic definition of logarithms and properties of logarithms.