Answer: 13
The rule you use is log(x/y) = log(x) - log(y)
So in this case, log(13/x) = log(13) - log(x) where the base is base 9
Notes:
The values of x and y must be positive.
The rule applies to any base as long as the base is positive and not equal to 1
The answer for the exponential expressions 1,2,3 and 4 will be
respectively.
<h3>What exactly is an exponent?</h3>
Exponential notation is a type of mathematical shorthand that allows us to write complex formulas in a more concise manner.
The basis of an exponent is a number or letter. It means that the base will be raised to a given level of power. The base is X, and the power is n.
The properties of the exponent used;
![\rm m^a \times m^b = m^{a+b} \\\\ m^a \times n^a = {mn}^a \\\\ m^a \times m^b = m^{a-b} \\\\ m^0 = 1](https://tex.z-dn.net/?f=%5Crm%20m%5Ea%20%5Ctimes%20m%5Eb%20%3D%20m%5E%7Ba%2Bb%7D%20%5C%5C%5C%5C%20m%5Ea%20%5Ctimes%20n%5Ea%20%3D%20%7Bmn%7D%5Ea%20%5C%5C%5C%5C%20m%5Ea%20%5Ctimes%20m%5Eb%20%3D%20m%5E%7Ba-b%7D%20%5C%5C%5C%5C%20m%5E0%20%3D%201)
Expression 1;
![\frac{(2.3^{-2})^2(5.3^2.2)^2}{(3)^-2(5.2)^2} \\\\ \frac{2^3.3^{-6}.5^2.3^6}{3^{-2}.5^2.2^2} \\\\ 4.5](https://tex.z-dn.net/?f=%5Cfrac%7B%282.3%5E%7B-2%7D%29%5E2%285.3%5E2.2%29%5E2%7D%7B%283%29%5E-2%285.2%29%5E2%7D%20%5C%5C%5C%5C%20%5Cfrac%7B2%5E3.3%5E%7B-6%7D.5%5E2.3%5E6%7D%7B3%5E%7B-2%7D.5%5E2.2%5E2%7D%20%5C%5C%5C%5C%204.5)
Expression 2;
![(3^3)(4^0)(3.2)^{-3}(2)^2 \\\\ 3^3.1.3^{-3}.2^{-3}.2^2 \\\\ \frac{1}{2}](https://tex.z-dn.net/?f=%283%5E3%29%284%5E0%29%283.2%29%5E%7B-3%7D%282%29%5E2%20%5C%5C%5C%5C%203%5E3.1.3%5E%7B-3%7D.2%5E%7B-3%7D.2%5E2%20%5C%5C%5C%5C%20%5Cfrac%7B1%7D%7B2%7D)
Expression 3;
![\frac{(3^7.4^7)(2.5)^{-3}(5)^2}{12^7.5^{-1}.2^{-4}} \\\\ \frac{3^7.4^7.25^{-3}.5^{-3}.5^2}{12^7.5^{-1}2^{-4}} \\\\ 2](https://tex.z-dn.net/?f=%5Cfrac%7B%283%5E7.4%5E7%29%282.5%29%5E%7B-3%7D%285%29%5E2%7D%7B12%5E7.5%5E%7B-1%7D.2%5E%7B-4%7D%7D%20%5C%5C%5C%5C%20%5Cfrac%7B3%5E7.4%5E7.25%5E%7B-3%7D.5%5E%7B-3%7D.5%5E2%7D%7B12%5E7.5%5E%7B-1%7D2%5E%7B-4%7D%7D%20%5C%5C%5C%5C%202)
Expression 4;
![\frac{(2.3)^{-1}.2^0}{(2.3)^{-1}}\\\\ \frac{2^{-1}.3^{-1}.1}{2.3}\\\\ 1](https://tex.z-dn.net/?f=%5Cfrac%7B%282.3%29%5E%7B-1%7D.2%5E0%7D%7B%282.3%29%5E%7B-1%7D%7D%5C%5C%5C%5C%20%5Cfrac%7B2%5E%7B-1%7D.3%5E%7B-1%7D.1%7D%7B2.3%7D%5C%5C%5C%5C%201)
Hence, the answer for the exponential expressions 1,2,3, and 4 will be
respectively.
To learn more about exponents, see
brainly.com/question/5497425
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The nearest hundred for 3,486 is 3,500 since it would round up because it is closer to that hundred.
The area of a trapezoid is found using the formula, A = ½ (a + b) h, where 'a' and 'b' are the bases (parallel sides) and 'h' is the height (the perpendicular distance between the bases) of the trapezoid.