Free Printable LOGARIT

1.

log (x.y) = ?

a)

log(x).log(y)

b)

log(x) - log(y)

c)

x.log(y)

d)

log(x) + log(y)

2.

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

a)

$\log_ax-\log_ay$

b)

$\log_ax+\log_ay$

c)

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

d)

$\log_ay-\log_ax$

3.

$\log_2b^3=?$

a)

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

b)

$3\log_b2$

c)

$3\log_2b$

d)

$\log_6b$

4.

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

a)

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

b)

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

c)

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

d)

$\log_a2b$

5.

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

a)

$-\log_nm$

b)

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

c)

$\frac{1}{\log_nm}$

d)

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

6.

$\log_mn\times\log_nk=?$

a)

$\log_mk$

b)

$\log_km$

c)

$\log_nk$

d)

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

7.

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

a)

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

b)

$\log_636\times5\log_6m\times3\log_6n$

c)

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

d)

$2+5\log_6m+3\log_6n$

8.

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

a)

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

b)

$\ln3-\ln2x-\ln1$

c)

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

d)

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

9.

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

a)

$\log\left(\frac{9x\times3z}{6y}\right)$

b)

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

c)

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

d)

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

10.

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

a)

2a + 2b

b)

a + b

c)

2ab

d)

a + 2b

11.

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

a)

a + b

b)

3 + 3a + b

c)

$a^3+3b^{ }$

d)

9ab

12.

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

a)

$\frac{n}{m}$

b)

m + n

c)

$\frac{m}{n}$

d)

$m\times n$

13.

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

a)

$\frac{a}{b}$

b)

a.b

c)

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

d)

$\frac{b}{a}$

14.

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

a)

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

b)

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

c)

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

d)

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

15.

Simplify: $\log_cd\times\log_bc\times\log_ab$

a)

$\log_da$

b)

$\log_{abc}bcd$

c)

1

d)

$\log_ad$

16.

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

a)

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

b)

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

c)

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

d)

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

17.

Expand ln(4x)

a)

ln4 + lnx

b)

ln 4 - lnx

c)

ln4x

d)

ln 4 - x

18.

Solve ln 1

a)

10

b)

4

c)

0

d)

1

19.

Solve ln e

a)

10

b)

1

c)

5

d)

3

20.

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

a)

5lnx + ln2y

b)

lnx5y2

c)

5lnx + 2lny

d)

5lnx - 2lny

21.

condense 4ln7 + 2lnx

a)

ln7⁴x

b)

ln7x

c)

ln7x²

d)

ln7⁴x²

22.

logarit tự nhiên có cơ số bằng bao nhiêu?

a)

$1$

b)

$5$

c)

$10$

d)

$e$

23.

Evaluate:

\ln e^2=x

a)

$1$

b)

$2$

c)

$e$

d)

$4$

24.

Simplify e^ln(x)

a)

0

b)

1

c)

x

d)

8

25.

Condense

$\log_39+\log_33$

a)

$\log_312$

b)

$\log_327$

c)

$\log_39$

LOGARIT

Total questions: 25

Worksheet time: 39mins

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