Choose two of the angles on ∆ABC, and locate the line segment between them. Draw a new line segment,DE , parallel to the line se
gment you located on ∆ABC. You can draw of any length and place it anywhere on the coordinate plane, but not on top of ∆ABC. From points D and E, create an angle of the same size as the angles you chose on ∆ABC. Then draw a ray from D and a ray from E through the angles such that the rays intersect. You should now have two angles that are congruent to the angles you chose on ∆ABC. Label the point of intersection of the two rays F, and draw ∆DEF by creating a polygon through points D, E, and F.
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You can use the definition of logarithm and the fact that a positive number raised to any power will always stay bigger than 0.
The domain of the given function is {x | x > 1 and a real number }
The range of the given function is (set of real numbers)
If a is raised to power b is resulted as c, then we can rewrite it that b equals to the logarithm of c with base a.
Or, symbolically:
Since c was the result of a raised to power b, thus, if a was a positive number, then a raised to any power won't go less or equal to zero, thus making c > 0
<h3>How to use this definition to find the domain and range of given function?</h3>Since log(x-1) is with base 10 (when base of log isn't specified, it is assumed to be with base 10) (when log is written ln, it is log with base e =2.71828.... ) thus, we have a = 10 > 0 thus the input x-1 > 0 too.
Or we have:
x > 1 as the restriction.
Thus domain of the given function is {x | x > 1 and a real number }
Now from domain, we have:
(log(x-1) > -infinity since log(0) on right side have arbitrary negatively large value which is denoted by -infinity)
Thus, range of given function is whole real number set (since all finite real numbers are bigger than negative infinity)
Thus, the domain of the given function is {x | x > 1 and a real number }
The range of the given function is (set of real numbers
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