Log Laws

Log Laws

Quick Review of Exponent Rules

Product Rule with Logs

 $\log\left(MN\right)$  

Multiple Choice

Expand:  $\log\ ab$  

•  $\log a\ -\ \log b$  

•  $b\log a$  

•  $a\log b$  

•  $\log a+\log b$  

Multiple Choice

Expand:  $\log_63x$  

•  $\log_63\ +\ \log_6x$  

•  $\log_63-\log_6x$  

•  $3\log_6x$  

•  $x\log_63$  

Multiple Choice

Condense the following logarithm: lnx + ln4

• ln 4x

• ln 4/x

• log 4 + log x

• ln x⁴

Multiple Choice

Expand: ln(4xy)

• ln4+lnx+lny

• 4lnxy

• 4lnx+lny

• 4ln(x+y)

Quotient Rule with Logs

 $\log\left(\frac{M}{N}\right)$  

Multiple Choice

Expand: $\log\left(\frac{9}{4}\right)$  

• log9+log4

• log(9-4)

• log9-log4

• log4-log9

Multiple Choice

Expand.

• A

• B

• C

• D

Multiple Choice

Fully simplify.

• A

• B

• C

• D

Power Rule with Logs

 $\log x^2$  

Multiple Choice

Rewrite log_b(xⁿ)

• nlog_bx

• (log_bx)ⁿ

• xⁿlog_bx

• log_b(xⁿ)

Multiple Choice

Which of the logarithms below is equivalent to the following:
 $2\log12$  

• log 10

• log 6

• log 24

• log 144

Multiple Choice

Use the properties of logarithms to retwrite

• A

• B

• C

• D

Expand:
 $\log\left(\frac{5x^2}{y^3}\right)$   

Condense:  $2\log6+3\log x-\log y-2\log z$  

Multiple Choice

Expand: ln(4xy)

• ln4+lnx+lny

• 4lnxy

• 4lnx+lny

• 4ln(x+y)

Multiple Choice

Expand: log(3x)²

• 2log(3+x)

• 2log3+logx

• log3+2logx

• 2(log3+logx)

Multiple Choice

Expand:  $\log\left(\frac{8x}{yz}\right)\$  

• log8+logx-logy-logz

• log8+logx-logy+logz

• log(8x)-log(yz)

• 8logx-ylogz

Multiple Choice

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

• ln2+2lnx+lny+4lnz

• ln2+2lnx+lny-4lnz

• 2ln(2xy)-4lnz

• 2ln2x+lny-4lnz

Multiple Choice

Condense: log16 + log2 - log8

• log4

• log8

• log10

• log24

Multiple Choice

• log (xy³)

• log (x⁶ − y³)

• log (x⁶/y³)

• log (x⁶ + y³)

Multiple Choice

• ln(wvu⁵)

• ln(u + v + w⁵)

• ln(uvw⁵)

• ln(uvw)⁵