Log laws

Logarithms to base 10

Rules

Examples

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

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

• log9+log4

• log(9-4)

• log9-log4

• log4-log9

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

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

Condense: log16 + log2 - log8

• log4

• log8

• log10

• log24

Multiple Choice

• log (xy³)

• log (x⁶ − y³)

• log (x⁶/y³)

• log (x⁶ + y³)

Multiple Choice

Solve

$$3\log_82-\log_84=\log_8g$$  

• 2

• 4

• 8

• 12

Multiple Choice

Solve

$$\log_3y=-\log_316+\frac{1}{3}\log_364$$  

• 4

• 16

• 1/4

• 1/2