7-5 to 7-7 Logarithms by Kaitlyn and Yebon!

Multiplying Logs

100

Solve the equation for x 

log₃6 + log₃x = log₃12

What is x=2

log₃6x=log₃12

6x=12

x=2

200

log₆x + log₆(x - 9) = 2

What is x=12

log₆ X(x-9) = 2 

x² - 9x= 6²

x²-9x-36

(x - 12)(x + 3)= 0 

Check 

x=12

300

Solve the equation for x

log₆ .1 + 2log₆x= log₆2 + log₆5 

What is x=10 

log₆ .1x²=log₆10 

.1x²=10 

x²=100

x=10

400

State if the equation is true or false.

log₅22x= log₅ 22 + log₅x

What is true? 

22x=x (22) 

500

Solve log₃(a²  + 3) + log₃3= 3

What is a= square root of 6 

log₃(a²+3) + log₃3 =3

log₃3(a² + 3) = 3 

3(a²+ 3) = 3³

3a²+ 9 = 27

3a²= 18

a²=6 

a= square root of 6

Dividing Logarithms

100

State whether the equation is true or false. 

log₈x - log₈3= log₈(x-3)

What is false?
The equation is division so the equation would be log₈x/log₈3

200

Solve equation log₇ 100 - log₇ (y+5) = log₇10

What is y= 5

Log7100/Log7(y+5)= Log710

100/y+5 = 10 

100= 10(y + 5) 

100= 10y + 50 

50= 10y 

y=5

300

Solve the equation for x 

log₁₀18 - log₁₀3x= log₁₀2

what is x=3 

3x*(log₁₀ 18/3x= log₁₀2)

18=6x 

x=3

400

Solve the equation for y: 

log₄ (2y+2) - log₄(y-2) = 1

What is y=5

log₄ (2y+2)/ (y-2) = 1 

(2y+2)/ (y-2)= 4¹

2y+2= 4(y-2)

2y + 2= 4y - 8 

2= 2y - 8 

2y=10 

y=5

500

Solve the equation for b: log₂(15b - 15) - log₂ (-b2 + 1) = 1

what is no solution 

Explanation 

:No negative logs EVER

Common Logs

100

Evaluate the below expression with your calculator and round to the nearest thousandth:

log5

What is .699 

Explanation: Use a calculator.

200

Evaluate the below expression with your calculator and round to the nearest thousandth:

log21

What is 1.322

Explanation: Use a calculator.

300

Evaluate the below expression with your calculator and round to the nearest thousandth:

log451

What is 2.654

Explanation: Use a calculator.

400

Evaluate the below expression with your calculator and round to the nearest thousandth:

log(1/4)

What is -.060

Explanation: Use a calculator.

500

Solve for x. Use your calculator for the solution and round to the nearest thousandth.

6^x + 2 = 21

What is x= - 0.301 

Explanation:

log6^x + 2= 21

(x+2)log6= log21

x+2= log21/log6

x=log21/log6 -2 

x=- 0.301

Base e and Natural Logs

100

Evaluate the below expression with your calculator and round to the nearest thousandth:

e ^-1.5

What is 

e ^-1.5 ≈ 0.2231

Explanation: Use a calculator.

200

Evaluate the below expression with your calculator and round to the nearest thousandth:

ln 0.4 

What is 

ln 0.4 ≈ -0.9163

Explanation: Use a calculator.

300

Evaluate the below expression with your calculator and round to the nearest thousandth:

(ln e)/5 

What is 1/5 

Explanation: Use a calculator. 

400

Solve for x. Use your calculator for the solution and round to the nearest thousandth. 

e^3x=9

What is x= .732

Explanation:

e^3x=9

lne^3x=ln 9

3xln e= ln 9

3x=ln 9  

x= 1/3 ln 9 

x=0.732

500

Solve for x. Use your calculator for the solution and round to the nearest thousandth. 

e^20x=15

What is x= .135

Explanation:

e^20x=15

ln e^20x=ln 15

20xln e=ln 15

20x = ln 15  

x = (1/20)ln 15 

x = 0.135