Generalize logarithmic coincidences After playing around with logarithms, I've found the following coincidences: log_(10)2~~0.3, since 2^(10)~~10^3, and log_(10)5~~0.7, since 5^(1000)~~10^(700). I'm sure these are well known. I was just wondering if there was a method or algorithm to generalize these "coincidences" to any base or number. I only have a basic understanding of number theory and would like to learn more.

$\frac{20b}{{\left(4b^3\right)}^3}$

Which operation could we perform in order to find the number of milliseconds in a year??
${\displaystyle 60\cdot 60\cdot 24\cdot 7\cdot 365}$
${\displaystyle 1000\cdot 60\cdot 60\cdot 24\cdot 365}$
${\displaystyle 24\cdot 60\cdot 100\cdot 7\cdot 52}$
${\displaystyle 1000\cdot 60\cdot 24\cdot 7\cdot 52?}$

Tell about the meaning of Sxx and Sxy in simple linear regression,, especially the meaning of those formulas

Is the number 7356 divisible by 12? Also find the remainder.
A) No
B) 0
C) Yes
D) 6

What is a positive integer?

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149600000000 is equal to
A)$1.496\times <!--\; \times \; -->{10}^{11}$
B)$1.496\times <!--\; \times \; -->{10}^{10}$
C)$1.496\times <!--\; \times \; -->{10}^{12}$
D)$1.496\times <!--\; \times \; -->{10}^8$

Find the value of$\log 1$ to the base $3$ ?

What is the square root of 3 divided by 2 .

write ${\displaystyle \sqrt[5]{{\left(7x\right)}^4}}$ as an equivalent expression using a fractional exponent.

simplify ${\displaystyle \sqrt{125n}}$

What is the square root of ${\displaystyle \frac{144}{169}}$