A Nice Algebra Equation | Math Olympiad Problem

In todays video, I will be teaching you how to solve an interesting problem. Make sure to like, subscribe, and also comment any questions or video ideas you may have relating to math!
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[KristOFF-T]

You can just do
log(70) / log(7) = 2.183...
and
log(80) / log(8) = 2.107...

This works with any base too.
You said log(10) is 1, so the base you used is 10.
Yes, "log" commonly refers to the base 10 logarithm, but in practical applications, bases like {
a) e (Euler's number = ~2.718)
- e-based log is also called natural logarithm
- most of the time written as "ln"
- but sometimes "log" refers to this
- appears across various fields
- 10 is a pretty random number, but e has pretty unique unique mathematical properties, which make it easier to use
- in python, the "log" function is actually the natural logarithm
b) 2
- useful in computer science
- most of the time written as "log_2", but sometimes just log in the context of CS
} are simply more convenient.

Or if your calculator allows inputting the base of the logarithm, you can just do log_7(70) and log_8(80)
(But that's just syntactic sugar and I find it unnecessary and easier to just do "log(something) / log(base)")

[AlexanderSemashkevich]

x≈1+1/0.845≈369/169≈2.1834
Deviation is about 0.0001
7^2.1834≈70.01

[ii]

Olympiad problem? Seriously? This is not even a *_problem_* as such. This is a routine practice *_task_* for a student familiar with logarithm manipulation.