Quiz about LOGARIT

Question 1

log (x.y) = ?

Accepted Answer

log(x) + log(y)

Answer

log(x).log(y)

Answer

log(x) - log(y)

Answer

x.log(y)

Question 2

$$\log_a\left(\frac{y}{x}\right)=?$$

Accepted Answer

$$\log_ay-\log_ax$$

Answer

$$\log_ax-\log_ay$$

Answer

$$\log_ax+\log_ay$$

Answer

$$\frac{\log_ax}{\log_ay}$$

Question 3

$$\log_2b^3=?$$

Accepted Answer

$$3\log_2b$$

Answer

$$\frac{1}{2}\log_2b$$

Answer

$$3\log_b2$$

Answer

$$\log_6b$$

Question 4

$$\log_{a^2}\left(b\right)=?$$

Accepted Answer

$$\frac{1}{2}\log_{\left|a\right|}b$$

Answer

$$\frac{1}{2}\log_ab$$

Answer

$$2\log_{\left|a\right|}b$$

Answer

$$\log_a2b$$

Question 5

The change of base property states that: $$\log_mn=?$$

Accepted Answer

$$\frac{\ \log_kn}{\log_km}$$

Answer

$$-\log_nm$$

Answer

$$\frac{1}{\log_nm}$$

Answer

$$\frac{\ \log_km}{\log_kn}$$

Question 6

$$\log_mn imes\log_nk=?$$

Accepted Answer

$$\log_mk$$

Answer

$$\log_km$$

Answer

$$\log_nk$$

Answer

$$\log_m\left(k.n\right)$$

Question 7

Expand completely: $$\log_6\left(36m^5n^3\right)$$

Accepted Answer

$$2+5\log_6m+3\log_6n$$

Answer

$$\log36+5\log m+3\log n$$

Answer

$$\log_636 imes5\log_6m imes3\log_6n$$

Answer

$$2+\log_6m^5+\log_6n^3$$

Question 8

Expand completely: $$\ln\left(\frac{3}{2x+1}\right)$$

Accepted Answer

$$\ln3-\ln\left(2x+1\right)$$

Answer

$$\ln3+\ln\left(2x+1\right)$$

Answer

$$\ln3-\ln2x-\ln1$$

Answer

$$\ln3-\ln2-\ln x-\ln1$$

Question 9

Write the expression in condensed form: $$9\log x-6\log y+3\log z$$

Accepted Answer

$$\log\left(\frac{x^9z^3}{y^6}\right)$$

Answer

$$\log\left(\frac{9x imes3z}{6y} ight)$$

Answer

$$\log\left(\frac{x^9y^6}{z^3}\right)$$

Answer

$$-\log\left(x^9y^6z^3\right)$$

Question 10

Let $$\log5=a;\log2=b$$ . $$\log100=?$$

Accepted Answer

2a + 2b

Answer

a + b

Answer

2ab

Answer

a + 2b

Question 11

Let $$\log_23=a;\log_25=b.\ Then\ \log_21080\ =?$$

Accepted Answer

3 + 3a + b

Answer

a + b

Answer

$$a^3+3b^{ }$$

Answer

9ab

Question 12

Let $$\log_25=m;\ \log_27=n.$$ Then $$\log_57=?$$

Accepted Answer

$$\frac{n}{m}$$

Answer

m + n

Answer

$$\frac{m}{n}$$

Answer

$$m imes n$$

Question 13

Let $$\ln56=a;\ \ln8=b.$$ Then $$\log_{56}8=?$$

Accepted Answer

$$\frac{b}{a}$$

Answer

$$\frac{a}{b}$$

Answer

a.b

Answer

$$\frac{1}{a}+\frac{1}{b}$$

Question 14

Write the expression in condensed form: $$\frac{1}{3}\ln27-3\ln\left(2y\right)$$

Accepted Answer

$$\ln\left(\frac{3}{8y^3}\right)$$

Answer

$$\ln\left(\frac{9}{\left(2y\right)^3}\right)$$

Answer

$$\ln\left(\frac{3}{6y}\right)$$

Answer

$$\frac{1}{3}\ln\left(\frac{27}{8y^3}\right)$$

Question 15

Simplify: $$\log_cd imes\log_bc imes\log_ab$$

Accepted Answer

$$\log_ad$$

Answer

$$\log_da$$

Answer

$$\log_{abc}bcd$$

Answer

1

Question 16

Write the following expression in condensed form: $$\log_{\sqrt{\ 3}}a+\log_3b$$

Accepted Answer

$$\log_3\left(a^2b\right)$$

Answer

$$\log_3\left(a.b\right)$$

Answer

$$\log_3\left(\sqrt{a\ }.\ b\right)$$

Answer

$$\log_{\sqrt{3}}\left(a.b\right)$$

Question 17

Expand ln(4x)

Accepted Answer

ln4 + lnx

Answer

ln 4 - lnx

Answer

ln4x

Answer

ln 4 - x

Question 18

Solve ln 1

Accepted Answer

0

Answer

10

Answer

4

Answer

1

Question 19

Solve ln e

Accepted Answer

1

Answer

10

Answer

5

Answer

3

Question 20

Expand $$\ln\ x^5y^2$$

Accepted Answer

5lnx + 2lny

Answer

5lnx + ln2y

Answer

lnx5y2

Answer

5lnx - 2lny

Question 21

condense 4ln7 + 2lnx

Accepted Answer

ln74x2

Answer

ln74x

Answer

ln7x

Answer

ln7x2

Question 22

Evaluate:

$$\ln e^2=x$$

Accepted Answer

$$2$$

Answer

$$1$$

Answer

$$e$$

Answer

$$4$$

Question 23

Simplify e^ln(x)

Accepted Answer

x

Answer

0

Answer

1

Answer

8

Question 24

Condense

$$\log_39+\log_33$$

Accepted Answer

$$\log_327$$

Answer

$$\log_312$$

Answer

$$\log_39$$

LOGARIT

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