Logarithms

Log vs. Exponential

100

Rewrite the following function in the opposite form.

log₈1=0

8⁰=1

200

Rewrite the following function in the opposite form.

 log₃(1/27)=-3

3^-3=(1/27)

300

Rewrite the following function in the opposite form.

10³=1000

log1000=3

400

Rewrite the following function in the opposite form.

9^(1/2)=3

log₉3=(1/2)

500

Rewrite the following function in the opposite form.

log₁₀₀(1/10)=-(1/2)

100^(-1/2)=(1/10)

Expanding Logs

100

Completely expand the following logarithms. (Answers have no exponents, multiplication or division)

log₄(20/x³)

log₄20 - 3log₄x

200

Completely expand the following logarithms. (Answers have no exponents, multiplication or division)

log3c³g

log(3) + 3log(c) +log(g)

300

Completely expand the following logarithms. (Answers have no exponents, multiplication or division)

log₅4(x)^1/3

log₅4 + (1/3)log₅(x)

400

Completely expand the following logarithms. (Answers have no exponents, multiplication or division)

ln(x³/2z²)

3ln(x)-log(2)-2log(z)

500

Completely expand the following logarithms. (Answers have no exponents, multiplication or division)

log(y^2/3/3z³x^1/5)

(2/3)log(y) -log (3) -3log(z)- (1/5)log (x)

Prop. of Logs

100

Use the properties of logarithms to write each of the following as a single logarithm. SIMPLIFY!

3log₅x-log₅4

log₅(x³/4)

200

Use the properties of logarithms to write each of the following as a single logarithm. SIMPLIFY!

log₄x+log₄(x -6)

log₄(x²-6x)

300

Use the properties of logarithms to write each of the following as a single logarithm. SIMPLIFY!

6ln(2)-4ln(y)

ln(64/y⁴)

400

Use the properties of logarithms to write each of the following as a single logarithm. SIMPLIFY!

log₃6-4log₃y+2log₃x

log₃(6x²/y⁴)

500

Use the properties of logarithms to write each of the following as a single logarithm. SIMPLIFY!

3lnx-4lny-8lnz

ln(x³/y⁴z⁸)

Evaluate the Log

100

Evaluate the following log.

log₂16

4

200

Evaluate the following log. 

ln(e¹⁰)

10

300

Evaluate the following log. 

log₄(1/64)

-3

400

Evaluate the following log. 

log(0.1)

-1

500

Evaluate the following log. 

log₅(1/125)

-3

Solve for x!

100

Solve the following equations for x. 

log₄₉7=x

x= 1/2

200

Solve the following equations for x. 

4^x+2=8

x=(-1/2)

300

Solve the following equations for x. 

log_bb=x

x=1

400

Solve the following equation for x. Round to the nearest hundredth if necessary. 

e^x+1=8

x=1.08

500

Solve the following equation for x. Round to the nearest hundredth if necessary. 

log_x(6x+27)=2

x=9