Quiz about Logarithm Laws

Question 1

Evaluate $$2\left(\log2\ +\ \log3\right)$$

Accepted Answer

$$\log\ 36$$

Answer

$$\log_26$$

Answer

$$\log_{ }10$$

Answer

$$\log_{ }13$$

Question 2

Evaluate $$\log_36-\log_32-\log_33$$

Accepted Answer

$$0$$

Answer

$$1$$

Answer

$$\log_33$$

Answer

$$\log_26$$

Question 3

Evaluate $$\log_3\frac{3}{81}$$

Accepted Answer

$$-3$$

Answer

$$3$$

Answer

no answer

Answer

4

Question 4

Evaluate

$$\log_44^3$$

Accepted Answer

$$3$$

Answer

$$1$$

Answer

$$-3$$

Answer

$$64$$

Question 5

Express into a single logarithm:

$$\frac{1}{3}\left(4\log_bx-2\log_by\right)$$

Accepted Answer

$$\log_b\sqrt[3]{\frac{x^4}{y^2}}$$

Answer

$$\log_b\left(\frac{x^4}{y^2}\right)^3$$

Answer

$$\log_b\sqrt[3]{\frac{2x}{y}}$$

Answer

$$\frac{2}{3}\log_bx^4y^2$$

Question 6

Express into a single logarithm:

$$\log_{ }xy\ -\frac{1}{2}\log x$$

Accepted Answer

$$\log\ \sqrt{x}y$$

Answer

$$\log\ \frac{y}{\sqrt{x}}$$

Answer

$$\log\ \sqrt{xy}$$

Answer

$$\log\ \frac{y}{2}$$

Question 7

Express into a single logarithm

$$y\left(\frac{1}{2}\log_b3+\frac{1}{2}\log_bx\right)$$

Accepted Answer

$$\log_b\left(\sqrt{3x}\right)^y$$

Answer

$$\log_b\ \frac{3xy}{2}$$

Answer

$$\log_b\ \frac{\left(3x\right)^y}{2}$$

Answer

$$\log_b\ \frac{3x}{2y}$$

Logarithm Laws