Free Printable Logarithms Review for Calculus

1.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

2.

Exponential functions are the inverse of...

a)

Linear Functions

b)

Polynomial Functions

c)

Quadratic Functions

d)

Logarithmic Functions

3.

Which number(s) are the most common bases for logarithms?

a)

$1$

b)

$10$

c)

$e$

d)

$\pi$

4.

Which logarithmic properties do you remember learning about in previous courses?

a)

Product Property

b)

Quotient Property

c)

Power Property

d)

Change of Base Property

5.

Which of the following illustrates the Product Property of Logarithms?

a)

$\log_3\left(x\right)+\log_3\left(y\right)=\log_3\left(x+y\right)$

b)

$\log_3\left(x\right)\cdot\log_3\left(y\right)=\log_3\left(xy\right)$

c)

$\log_3\left(x\right)+\log_3\left(y\right)=\log_3\left(xy\right)$

d)

$\log_3\left(x\right)\cdot\log_3\left(y\right)=\log_3\left(x+y\right)$

6.

Which of the following illustrates the Quotient Property of Logarithms?

a)

$\log_4\left(x\right)-\log_4\left(y\right)=\log_4\left(x-y\right)$

b)

$\log_4\left(x\right)\div\log_4\left(y\right)=\log_4\left(\frac{x}{y}\right)$

c)

$\log_4\left(x\right)-\log_4\left(y\right)=\log_4\left(\frac{x}{y}\right)$

d)

$\log_4\left(x\right)\div\log_4\left(y\right)=\log_4\left(x-y\right)$

7.

Which of the following illustrates the Power Property of Logarithms?

a)

$\log_5\left(m^n\right)=n+\log_5\left(m\right)$

b)

$\log_5\left(m^n\right)=n\cdot\log_5\left(m\right)$

c)

$\log_5\left(m^n\right)=\log_5\left(n\cdot m\right)$

d)

$\log_5\left(m^n\right)=\log_{5n}\left(m\right)$

8.

Which of the following illustrates the Change of Base Property of Logarithms? (select all that apply)

a)

$\log_8\left(p\right)=\frac{\ln\left(p\right)}{\ln\left(8\right)}$

b)

$\log_8\left(p\right)=\ln\left(p\right)\cdot\ln\left(8\right)$

c)

$\log_8\left(p\right)=\ln\left(p\right)+\ln\left(8\right)$

d)

$\log_8\left(p\right)=\frac{\log\left(p\right)}{\log\left(8\right)}$

e)

$\log_8\left(p\right)=\frac{1}{\ln\left(8\right)}\cdot\ln\left(p\right)$

9.

Evaluate (without using your GDC): $\log_525$

(a)

10.

Simplify: $\ln\left(e^{4x}\right)$

(a)

11.

Evaluate (without using your GDC): $\log_9\left(3\right)$

(a)

12.

Expand the logarithm: $\log_5\left(u\cdot v\cdot w^3\right)$

a)

$3\log_5\left(u\right)\cdot3\log_5\left(v\right)\cdot3\log_5\left(w\right)$

b)

$\log_5\left(u\right)\cdot\log_5\left(v\right)\cdot3\log_5\left(w\right)$

c)

$\log_5\left(u\cdot v\cdot3w\right)$

d)

$\log_5\left(u\right)+\log_5\left(v\right)+3\log_5\left(w\right)$

13.

Expand the logarithm: $\log_3\sqrt{xyz}$

a)

$\frac{1}{2}\log_3\left(x+y+z\right)$

b)

$\frac{1}{2}\log_3\ x+\log_3\ y+\log_3\ z$

c)

$\frac{1}{2}\left(\log_3\ x+\log_3\ y+\log_3\ z\right)$

d)

$\sqrt{\log_3\left(xyz\right)}$

14.

Expand the logarithm: $\log_8\left(xy^5\right)^2$

a)

$2\log_8\left(x\right)+10\log_8\left(y\right)$

b)

$10\log_8\left(x\right)+10\log_8\left(y\right)$

c)

$2\log_8\left(x\right)\cdot10\log_8\left(y\right)$

d)

$2\log_8\left(x\right)+5\log_8\left(y\right)$

15.

Expand the logarithm: $\ln\left(\frac{x}{y^2}\right)^4$

a)

$\frac{4\ln\left(x\right)}{8\ln\left(y\right)}$

b)

$4\ln\left(x\right)-4\ln\left(y\right)$

c)

$4\ln\left(x-y^2\right)$

d)

$4\ln\left(x\right)-8\ln\left(y\right)$

16.

Overall, how confident do you feel in your basic understanding of logarithms?

4 lines

Logarithms Review for Calculus

Total questions: 16

Worksheet time: 12mins

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