Quiz about Exponential Equations and Intro to Logarithms Assessment

Question 1

Condense into a single logarithm.

$$\log_515+3\cdot\log_53$$

Accepted Answer

$$\log_5405$$

Answer

$$\log_{40}5$$

Answer

$$\log_{ }\frac{ ext{}x^5}{ ext{}y^3}$$

Answer

$$\log_3x^{11}$$

Question 2

Condense into a single logarithm.

$$\log_7272-\frac{1}{2}\cdot\log_764$$

Accepted Answer

$$\log_734$$

Answer

$$\log_{34}7$$

Answer

$$\log_{ }\frac{ ext{}3^5}{ ext{}\left(y-2 ight)^3}$$

Answer

$$\log_3x^{11}$$

Question 3

Expand the logarithm.

$$\log_4\left(3z^2\right)^4$$

Accepted Answer

$$4\log_4\left(3\right)+8\log_4\left(z\right)$$

Answer

$$12+\log_4\left(6z\right)$$

Answer

$$1+2\log_4\left(12z\right)$$

Question 4

Expand the logarithm.

$$\log_{10}\left(\frac{ ext{x}^5}{ ext{y}^3} ight)^2$$

Accepted Answer

$$10\log_{10}\left(x\right)-6\log_{10}\left(y\right)$$

Answer

$$5\log_5\left(x\right)+3\log_2\left(y\right)$$

Answer

$$4\log_{ }\left(x^5\right)-3\log_{ }\left(y^3\right)$$

Answer

$$\log_xy+\log_yx$$

Question 5

Select the correct expression in logarithmic form.

$$3^{-3}=\frac{1}{27}$$

Accepted Answer

$$\log_3\ \frac{1}{27}=-3$$

Answer

$$\log_{-3}27=1$$

Answer

$$\log_3\frac{-1}{27}=3$$

Answer

l $$\log_{27}-3=1$$

Question 6

Select the correct expression in logarithmic form.

$$7^x=12$$

Accepted Answer

$$\log_712=x$$

Answer

$$\log_{-7}x=12$$

Answer

$$\log_7\frac{-x}{12}=0$$

Answer

$$\log_{12}7=x$$

Exponential Equations and Intro to Logarithms Assessment