Free Printable logarithms & index

1.

Rewrite as an exponential: $\log_7\left(\frac{1}{49}\right)=-2$

a)

$7^{\frac{1}{49}}=-2$

b)

$\left(\frac{1}{49}\right)^{-2}=7$

c)

$7^{-2}=\frac{1}{49}$

d)

$\left(-2\right)^7=\frac{1}{49}$

2.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

3.

Nilai dari $\log_r\left(\frac{1}{p^5}\right)\times\log_q\left(\frac{1}{r^3}\right)\times\log_p\left(\frac{1}{q}\right)=.....$

a)

-15

b)

-5

c)

-3

d)

1/15

e)

5

4.

Jika $\log_23=a$ dan $\log_37=b$ , maka $\log_{21}56=.....$

a)

$\frac{a\left(b+2\right)}{a+b}$

b)

$\frac{b\left(a+2\right)}{a+b}$

c)

$\frac{3+ab}{a+ab}$

d)

$\frac{3a+b}{a+b}$

e)

$\frac{2a+3b}{a-b}$

5.

Use multiple log properties to write as a single log:
log₂x - 5log₂y

a)

log₂(x/y⁵)

b)

log₂(xy⁵)

c)

log₂(x/y)⁵

d)

log₂(x/5y)

6.

Rewrite 1.6^(x+2) = 14.1

a)

log_1.614.1 = x+2

b)

log_1.6(x+2) = 14.1

c)

log_14.1(x+2) = 1.6

d)

log_(x+2)1.6 = 14.1

7.

Solve the following for 'x';
log₆(3x - 2) = log₆(5x - 8)

a)

x = 3

b)

x = 2

c)

x = -1

d)

No Solution

8.

Solve.

9(e^x)- 31 =23

a)

x = 1.79

b)

x = 4.21

c)

x = -3.5

d)

x = 1.27

9.

Solve:

log(x) + log(x+3) = 1

a)

5

b)

-2

c)

-5

d)

2

10.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

11.

Solve:

ln(x+8) - ln (8) = 3

a)

152.68

b)

188.77

c)

4.24

d)

8.01

12.

Solve for f:
$\log_6\left(f-4\right)=\log_6\left(6f+26\right)$

a)

f = -5

b)

f = 5

c)

f = 6

d)

f = -6

13.

log(xy²)

a)

logx+2logy

b)

logx+logy²

c)

logx-2logy

d)

logx+logy+log2

14.

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

15.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

16.

Condense the following logarithm: 3 log₂x + 2 log₂y – 4 log₂z

a)

log₂x³y²∕z⁴

b)

log₂x³y²z⁴

c)

log₂xyz⁹

d)

9log₂xyz

17.

Which expression is equivalent to $\log_{ }4n^3$ ?

a)

$3\left(\log4\ +\log n\right)$

b)

$3\cdot\log4\ +\log n$

c)

$\log4+3\cdot\log n$

d)

$\log64+3\cdot\log n$

18.

Write as a single logarithm: $\log_6\left(x-3\right)+\log_6x$

a)

$\log_6\left(x^2-3x\right)$

b)

$\log_6\left(2x-3\right)$

c)

$\log_{12}\left(x^2-3x\right)$

d)

$\log_6\left(-x\right)$

19.

Logarithms are the inverse of ___________.

a)

Trees

b)

Quadratics

c)

Square

d)

Exponential

20.

Condense: $\log\ x\ -\left(3\log y+2\log z\right)$

a)

$\log\ \frac{x}{y^3z^2}$

b)

$\log\ xy^3z^2$

c)

$\log\ \frac{xy^3}{z^2}$

d)

$\log\ \frac{x}{5yz}$

logarithms & index

Total questions: 20

Worksheet time: 24mins

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