Quiz about logarithms

Question 1

Rewrite 3⁴ = 81 in logarithmic form.

Accepted Answer

log₃81 = 4

Answer

log₃4 = 81

Answer

log₈₁3 = 4

Answer

log₄81 = 3

Answer

$$\frac{\log81}{\log3^4}$$

Question 2

The common logarithm has what base?

Accepted Answer

10

Answer

0

Answer

e

Answer

-e

Question 3

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

Accepted Answer

log (12x²)

Answer

log (12 + 2x)

Answer

log (14x)

Answer

log (24x)

Question 4

Simplify the expression
log(30)-log(6)

Accepted Answer

log(5)

Answer

-6log(30)

Answer

log(24)

Answer

log(-24)

Question 5

ln(-.56)=

Accepted Answer

undefined

Answer

-.580

Answer

.580

Answer

-4.025

Question 6

Describe the transformation of y=ln(x) that would give the graph for y = ln(x+7)

Accepted Answer

horizontal translation 7 left

Answer

vertical translation 7 up

Answer

vertical translation 7 down
vertical stretch by a factor of 7

Answer

horizontal translation 7 right

Question 7

Describe the transformation of y=ln(x) that would give the graph for y = 7ln(x)

Accepted Answer

vertical stretch by a factor of 7

Answer

vertical translation 7 up

Answer

vertical compression by a factor of 7

Answer

horizontal translation 7 left

Question 8

Describe the transformation of y=ln(x) that would give the graph for y = ln(-x)

Accepted Answer

reflection over the y-axis

Answer

reflection over the line y=x

Answer

reflection over the x-axis

Answer

reflection over the line y=-1

Question 9

Evaluate the log:
log₃(1/9) =

Accepted Answer

-2

Answer

1/2

Answer

2

Answer

3

Question 10

Rewrite log_pt = m in exponential form.

Accepted Answer

pm = t

Answer

pt = m

Answer

tm = p

Answer

mt = p

Question 11

Solve by changing to exponential form:

log x = -4

Accepted Answer

x = .0001

Answer

x = .001

Answer

x = 10

Answer

x = .01

Answer

x = -1/4

Question 12

$$f\left(x\right)=\frac{1}{5}\ln\left(x+7\right)$$

Which are transformations of f(x) from $$y=\ln\left(x\right)$$ ?

Accepted Answer

vertical shrink by 1/5

Accepted Answer

left 7

Answer

vertical stretch by 1/5

Answer

right 7

Answer

up 7

Question 13

$$f\left(x\right)=9\log_8\left(x\right)-2$$

Which are transformations of f(x) from $$y=\log_8\left(x\right)$$ ?

Accepted Answer

vertical stretch by 9

Accepted Answer

down 2

Answer

vertical shrink by 9

Answer

right 2

Answer

vertical stretch by 8

Question 14

Rewrite $$\log_53x$$ using change of base

Accepted Answer

$$\frac{\log3x}{\log5}$$

Answer

$$\frac{\log5}{\log\ 3x}$$

Answer

$$\log\left(\frac{3x}{5}\right)$$

Answer

$$\log15x$$

Answer

$$\log3x\ -\log\ 5$$

Question 15

Express as a sum or difference of logarithms, where there are no exponents on the argument other than 1.

$$\log x^9y^2$$

Accepted Answer

$$9\log x+2\log y$$

Answer

$$\log x^9+\log y^2$$

Answer

$$\log\left(x^9+y^2\right)$$

Answer

$$\log\left(18xy\right)$$

Question 16

Express as a sum or difference of logarithms, where there are no exponents on the argument other than 1.

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

Accepted Answer

$$8\ln x-\ln y$$

Answer

$$\ln x^8-\ln y$$

Answer

$$\ln\left(x^8-y\right)$$

Answer

$$\frac{8\ln x}{\ln y}$$

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