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Topic 14 Test Review Pt. 2

Total questions: 14

Worksheet time: 17mins

Name
Class
Date
1.

Rewrite using the Change of Base Rule.

 log648\log_648  

a)

 log6log48\frac{\log6}{\log48}  

b)

 log48log6\frac{\log48}{\log6}  

c)

 log8\log8  

d)

 log(486)\log\left(\frac{48}{6}\right)  

2.

Solve the following equation:

 log(5x)=log(2x+9)\log\left(5x\right)=\log\left(2x+9\right)  

a)

 x=97x=\frac{9}{7}  

b)

 x=6x=6  

c)

 x=4x=4  

d)

 x=3x=3  

3.

Condense the following logarithm:

 2ln(x)ln(y)2\ln\left(x\right)-\ln\left(y\right)  

a)

 ln(x2y)\ln\left(\frac{x^2}{y}\right)  

b)

 ln(x2y)\ln\left(x^2y\right)  

c)

 ln(x2y)\ln\left(x^2-y\right)  

d)

 ln(x2+y)\ln\left(x^2+y\right)  

4.

Expand the following logarithmic expression:

 log65xy\log_65xy  

a)

 log65x+log6y\log_65x+\log_6y  

b)

 log65xy\log_65x-y  

c)

 log65+log6x+log6y\log_65+\log_6x+\log_6y  

d)

 log65log6xlog6y\log_65-\log_6x-\log_6y  

5.

Solve the following equation:

 3b=173^b=17  

a)

 b=1.578b=1.578  

b)

 b=2.579b=2.579  

c)

 b=4.783b=4.783  

d)

 b=3.987b=3.987  

6.

Rewrite using the Change of Base Rule:

 log22450\log_22450  

a)

 log2450log2\frac{\log2450}{\log2}  

b)

 log(24502)\log\left(\frac{2450}{2}\right)  

c)

 log1225\log1225  

d)

 log2448\log2448  

7.

Solve the following equation:

 log3(5x+2)=3\log_3\left(5x+2\right)=3  

a)

 x=295x=\frac{29}{5}  

b)

 x=75x=\frac{7}{5}  

c)

 x=275x=\frac{27}{5}  

d)

 x=5x=5  

8.

Condense the following logarithm.

 log2x+3log2y\log_2x+3\log_2y  

a)

 log2(xy3)\log_2\left(\frac{x}{y^3}\right)  

b)

 log2xy3\log_2x-y^3  

c)

 log2xy3\log_2xy^3  

d)

 log23xy\log_23xy  

9.

Expand the following logarithm.

 log5a3b4\log_5a^3b^4  

a)

 3log5a+4log5b3\log_5a+4\log_5b  

b)

 log5a3+log5b4\log_5a^3+\log_5b^4  

c)

 3log5a4log5b3\log_5a-4\log_5b  

d)

 log5a3log5b4\log_5a^3-\log_5b^4  

10.

Solve the following equation.
 ex5=5e^x-5=5  

a)

 x=1.609x=1.609  

b)

 x=5.778x=5.778  

c)

 x=2.303x=2.303  

d)

 x=3.098x=3.098  

11.

Solve the following equation.

 log2+logx=1\log2+\log x=1  

a)

 x=15x=\frac{1}{5}  

b)

 x=5x=5  

c)

 x=1.359x=1.359  

d)

 x=12x=12  

12.

Solve the following equation.

 3x=813^x=81  

a)

 x=3x=3  

b)

 x=27x=27  

c)

 x=78x=78  

d)

 x=4x=4  

13.

Expand the following expression:

 log35xy2\log_35xy^2  

a)

 log35+log3x+2log3y\log_35+\log_3x+2\log_3y  

b)

 log35x+2log3y\log_35x+2\log_3y  

c)

 log35x+log3y2\log_35x+\log_3y^2  

d)

 log35+log3x+log3y2\log_35+\log_3x+\log_3y^2  

14.

Condense the following expression:

 log2x+4log2y\log_2x+4\log_2y  

a)

 5log2xy5\log_2xy  

b)

 log2xy4\log_2xy^4  

c)

 log2(xy4)\log_2\left(\frac{x}{y^4}\right)  

d)

 log2(y42)\log_2\left(\frac{y^4}{2}\right)