Properties of Logarithms part 1

Properties of
Logarithms

Advanced Precalculus

Multiple Choice

Rewrite log₂8 = 3 in exponential form

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

Multiple Choice

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81

• log₈₁3 = 4

• log₃81 = 4

• log₄81 = 3

Multiple Choice

Write in exponential form

log₂32 = 5

• 2^-5 = 32

• 2³² = 5

• 2⁵ = 32

• 32⁵ = 2

Multiple Choice

Evaluate.
log₃81

• 4

• ¹/₄

• -4

• -¹/₄

Multiple Choice

Evaluate log₄1

• 1

• 0

• 4

• undefined

Multiple Choice

Expand: $$\log_bmn$$  

• $$\log_bm\ -\ \log_bn$$  

• $$\log_bm+\log_bn$$  

• $$m\log_bn$$  

• $$n\log_bm$$  

Multiple Choice

Expand: $$\log_63x$$  

• $$\log_63\ +\ \log_6x$$  

• $$\log_63-\log_6x$$  

• $$3\log_6x$$  

• $$x\log_63$$  

Multiple Choice

Expand: $$\log\ ab$$  

• $$\log a\ -\ \log b$$  

• $$b\log a$$  

• $$a\log b$$  

• $$\log a+\log b$$  

Multiple Choice

Expand: $$\log_b\ \frac{m}{n}$$  

• $$\log_bm\ -\log_bn$$  

• $$\log_bm\ +\ \log_b\ n$$  

• $$m\log_bn$$  

• $$n\log_bn$$  

Multiple Choice

Expand: $$\log_2\ \frac{5}{x}$$  

• $$\log_25\ +\ \log_2x$$  

• $$\log_2x-\log_25$$  

• $$\log_25-\log_2x$$  

• $$5\log_2x$$  

Multiple Choice

Expand: $$\log\ \frac{k}{d}$$  

• $$k\log d$$  

• $$\log k\ +\ \log\ d$$  

• $$\log\ k\ -\ \log d$$  

• $$\log d-\log k$$  

Multiple Choice

Expand: $$\log_b\ m^p$$  

• $$\log_bm\ +\ \log_bp$$  

• $$\log_bm-\log_bp$$  

• $$\log_bp-\log_bm$$  

• $$p\log_bm$$  

Multiple Choice

Expand: $$\log_7\ y^8$$  

• $$\log_7y\ +\ \log_78$$  

• $$\log_7y-\log_78$$  

• $$8\log_7y$$  

• $$\log_78+\log_7y$$  

Multiple Choice

Expand: $$\log\ d^{\ k}$$  

• $$\log k+\log d$$  

• $$\log d\ -\ \log\ k$$  

• $$\log k-\log d$$  

• $$k\log d$$  

Multiple Choice

Expand: $$\log_9\sqrt{23}$$  

• $$\frac{1}{2}\log_923$$  

• $$\log_9\left(\frac{1}{2}\right)-\log_923$$  

• $$\log_9\sqrt{2}+\log_9\sqrt{3}$$  

• $$\log_9\ \left(\frac{1}{2}\right)+\log_923$$  

Multiple Choice

Expand: $$\log\ \frac{k^3}{2}$$  

• $$3\log2\ -\ \log k$$  

• $$3\log k-\log2$$  

• $$3\log k+\log2$$  

• $$\log k-3\log2$$  

Multiple Choice

Expand: $$\log\ \frac{a}{b^3}$$  

• $$\log a\ -\ 3\log b$$  

• $$\log\ a\ -\ \log3b$$  

• $$3\log a-\log b$$  

• $$\log a+3\log b$$  

Multiple Choice

Expand: $$\log_74\sqrt{d}$$  

• $$\log_7\ 4\ -\ \frac{1}{2}\log_7\ d$$  

• $$4\log_7d\ +\log_7\ \frac{1}{2}$$  

• $$\log_7\ 4+\frac{1}{2}\log_7\ d$$  

• $$\frac{1}{2}\log4d$$  

Multiple Choice

Expand: $$\log x^3y^7$$  

• $$3\log x+7\log y$$  

• $$10\log xy$$  

• $$3\log x-7\log y$$  

• $$\log x^3+\log y^7$$  

Multiple Choice

Expand: $$\log\ 8h^2$$  

• $$\log64+\log\ h$$  

• $$\log8+2\log h$$  

• $$\log16+\log h$$  

• $$2\log8+\log h$$