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Desarrollar logaritmos: Propiedades

Total questions: 10

Worksheet time: 18mins

Name
Class
Date
1.

 log⁡(yx9)\log\left(yx^9\right)  

a)

 log⁡ y−9log⁡x\log\ y-9\log x  

b)

 log⁡ y−log⁡ 9+log⁡x\log\ y-\log\ 9+\log x  

c)

 log⁡ y+9log⁡x\log\ y+9\log x  

d)

 log⁡ y+log⁡x\log\ y+\log x  

2.

 log⁡(z8x)\log\left(z^8x\right)  

a)

 log⁡ z−8log⁡x\log\ z-8\log x  

b)

 8log⁡ z+log⁡x8\log\ z+\log x  

c)

 log⁡ z+8log⁡x\log\ z+8\log x  

d)

 log⁡ 8+log⁡ z+log⁡x\log\ 8+\log\ z+\log x  

3.

 log⁡(x7y2z)\log\left(\frac{x^7}{\sqrt{y^2z}}\right)  

a)

 7log⁡ x−22log⁡ y+log⁡z7\log\ x-\frac{2}{2}\log\ y+\log z  

b)

 7log⁡ x−2log⁡ y−log⁡z7\log\ x-2\log\ y-\log z  

c)

 7log⁡ x−log⁡ y+12log⁡z7\log\ x-\log\ y+\frac{1}{2}\log z  

d)

 7log⁡ x−22log⁡ y−12log⁡z7\log\ x-\frac{2}{2}\log\ y-\frac{1}{2}\log z  

4.

 log⁡(xy7z3)\log\left(\sqrt{\frac{xy^7}{z^3}}\right)  

a)

 12log⁡ x+72log⁡ y−3log⁡z\frac{1}{2}\log\ x+\frac{7}{2}\log\ y-3\log z  

b)

 12log⁡ x−72log⁡ y+32log⁡z\frac{1}{2}\log\ x-\frac{7}{2}\log\ y+\frac{3}{2}\log z  

c)

 12log⁡ x+72log⁡ y−32log⁡z\frac{1}{2}\log\ x+\frac{7}{2}\log\ y-\frac{3}{2}\log z  

d)

 12log⁡ x+7log⁡ y−3log⁡z\frac{1}{2}\log\ x+7\log\ y-3\log z  

5.

 log⁡(yz3x5)\log\left(\frac{\sqrt{yz^3}}{x^5}\right)  

a)

 12log⁡ y−3log⁡ z+5log⁡x\frac{1}{2}\log\ y-3\log\ z+5\log x  

b)

 12log⁡ y+32log⁡ z−5log⁡x\frac{1}{2}\log\ y+\frac{3}{2}\log\ z-5\log x  

c)

 12log⁡ y−32log⁡ z−log⁡x\frac{1}{2}\log\ y-\frac{3}{2}\log\ z-\log x  

d)

 12log⁡ y+3log⁡ z−log⁡ 5−log⁡x\frac{1}{2}\log\ y+3\log\ z-\log\ 5-\log x  

6.

 log⁡(x7zy3)\log\left(\frac{x^7}{z\sqrt{y^3}}\right)  

a)

 7log⁡ x−log⁡ z−3log⁡y7\log\ x-\log\ z-3\log y  

b)

 7log⁡ x−log⁡ z+32log⁡y7\log\ x-\log\ z+\frac{3}{2}\log y  

c)

 7log⁡ x−log⁡ z−13log⁡y7\log\ x-\log\ z-\frac{1}{3}\log y  

d)

 7log⁡ x−log⁡ z−32log⁡y7\log\ x-\log\ z-\frac{3}{2}\log y  

7.

 log⁡((x+8)3x5)\log\left(\sqrt{\frac{\left(x+8\right)^3}{x^5}}\right)  

a)

 32(log⁡ x+log⁡8)−52log⁡ x\frac{3}{2}\left(\log\ x+\log8\right)-\frac{5}{2}\log\ x  

b)

 32log⁡ (x+8)−52log⁡ x\frac{3}{2}\log\ \left(x+8\right)-\frac{5}{2}\log\ x  

c)

 32log⁡ (x+8)−5log⁡ x\frac{3}{2}\log\ \left(x+8\right)-5\log\ x  

d)

 32log⁡ x+log⁡ 8−52log⁡ x\frac{3}{2}\log\ x+\log\ 8-\frac{5}{2}\log\ x  

8.

 log⁡(6(x+4)3x5)\log\left(\frac{6\left(x+4\right)^3}{\sqrt{x^5}}\right)  

a)

 log⁡ 6+3log⁡ (x+4)−5log⁡x\log\ 6+3\log\ \left(x+4\right)-5\log x  

b)

 log⁡ 6+3log⁡ x+log⁡4−52log⁡x\log\ 6+3\log\ x+\log4-\frac{5}{2}\log x  

c)

 log⁡ 6+3log⁡ (x+4)−52log⁡x\log\ 6+3\log\ \left(x+4\right)-\frac{5}{2}\log x  

d)

 6log⁡ (x+4)−52log⁡x6\log\ \left(x+4\right)-\frac{5}{2}\log x  

9.

 log⁡(7ab35c2)\log\left(7ab^3\sqrt{5c^2}\right)  

a)

 log⁡7+log⁡a+3log⁡b+12log⁡5+22log⁡c\log7+\log a+3\log b+\frac{1}{2}\log5+\frac{2}{2}\log c  

b)

 log⁡7+log⁡a+log⁡b−12log⁡5−2log⁡c\log7+\log a+\log b-\frac{1}{2}\log5-2\log c  

c)

 log⁡7a+3log⁡b+12log⁡5+2log⁡c\log7a+3\log b+\frac{1}{2}\log5+2\log c  

d)

 log⁡7a+3log⁡b+12log⁡5c\log7a+3\log b+\frac{1}{2}\log5c  

10.

 log⁡ a2bc3\log\ \frac{a^2\sqrt{b}}{c^3}  

a)

 2log⁡a+12log⁡b+3log⁡c2\log a+\frac{1}{2}\log b+3\log c  

b)

 22log⁡a+12log⁡b+3log⁡c\frac{2}{2}\log a+\frac{1}{2}\log b+3\log c  

c)

 2log⁡a+12log⁡b−log⁡c2\log a+\frac{1}{2}\log b-\log c  

d)

 2log⁡a+12log⁡b−3log⁡c2\log a+\frac{1}{2}\log b-3\log c