Log Properties

Properties of Logs

by AnnMarie Winfield

Recall the ​Properties of Exponents

​Properties of Logs

​More examples

Multiple Choice

Expand

log(4x)

• log4-logx

• log4+logx

• 4logx

• xlog4

Multiple Choice

Expand

log(xy²)

• logx+2logy

• logx+logy²

• logx-2logy

• logx+logy+log2

Multiple Choice

$$Expand\ \log\left(\frac{x}{y}\right)$$  

• logx+logy

• xlogy

• log(x-y)

• logx-logy

Multiple Choice

$$Expand\ \log\left(\frac{m^3}{n}\right)$$  

• logm-log3-logn

• 3logm+logn

• 3logm-logn

• 3log(m-n)

Multiple Choice

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

• ln2+2lnx+lny+4lnz

• ln2+2lnx+lny-4lnz

• 2ln(2xy)-4lnz

• 2ln2x+lny-4lnz

Multiple Choice

• log (xy³)
• log (x⁶ − y³)
• log (x⁶/y³)
• log (x⁶ + y³)

Multiple Choice

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

• log (12 + 2x)

• log (14x)

• log (12 * 2x)

• log (12x²)

Multiple Choice

Using the change of base property, rewrite log₂31

• log(2) / log(31)

• log(2/31)

• log(31)/log(2)

• log(31/2)

Multiple Choice

Condense: log₂6+log₂3=

• log₂18

• log₂2 = 1

• log₂3

• log₂9

Multiple Choice

Logarithmic functions are the inverse of...

• Linear Functions
• Exponential Functions 
• Quadratic Functions 
• Polynomial Functions 

Multiple Choice

 The expression  $$\log\sqrt{xy}$$ is equivalent to

• $$2\log x\log y$$  

• $$2\left(\log x+\log y\right)$$  

• $$\frac{1}{2}\log x\log y$$  

• $$\frac{1}{2}\left(\log x+\log y\right)$$  

Multiple Select

$$\ln ab=\ln a+\ln b$$  

• True

• False