Logarithms
Exponential EQ's
Word Problems
Solving Exponential EQ's
Solving Log EQ's
100

Simplify the expression: 

log_2 8

3

100

Write the exponential equation 

4^5= 1,024

in logarithmic form.

log_4 1,024 = 5

100
If there are initially 3000 bacteria in a culture, and the number of bacteria increase by 25% each hour, how many bacteria will there be in 5 hours? Round to the nearest whole number.
What is 9,155 bacteria?
100

8^(2x)=8^(x+7)

x=7

100

log x = 3

1000

200

Write the equation 

log_3 729 = 6

in exponential form.

3^6=729

200

Write the exponential equation 

27^ (1/3) = 3

in logarithmic form.

log_27 3 = 1/3

200
If there are initially 3000 bacteria in a culture, and the number of bacteria increase by 25% each hour, after how many hours will you reach approximately 5,850 bacteria?
What is 3 hours?
200

25^(x-4)=5^(3x+1)

x = -9

200

log_3 x = 5

x = 243

300

Write the equation 

log 1000 = 3

in exponential form.

10^3=1000

300

Write the exponential equation 

(1/2)^-3=8

in logarithmic form.

log_(1/2) 8 = -3

300
Use the formula R = log I , where R is the measurement of the Richter scale and I is the intensity, to find the Richter scale measurement of an earthquake with intensity 30,000,000. Round your answer to four decimal places.
What is 7.4771?
300

e^(2x)=e^(x+4)

x = 4

300

Solve

ln x = 4 

Round your answer to two decimal places.

x ≈ 54.60

400

What is the asymptote of the graph of f(x) = log(x - 1) ?

x = 1

400

Is the graph 

y= 0.7^x

increasing or decreasing, and is it a function?

decreasing

400
Use the formula R = log I , where R is the measurement of the Richter scale and I is the intensity, to find the Richter scale measurement of an earthquake with intensity 35,000,000. Round your answer to four decimal places.
What is 7.5441 ?
400

3e^(3 - x)= 15

Round your answer to two decimal places.

x ≈ 1.39

400

3 ln x - 7 = 4

Round your answer to two decimal places.

x ≈ 39.12

500

What is the asymptote of the graph of f(x)= log(x + 2) -1 ?

x= -2

500

Simplify 

ln e^(3x)

3x

500
Use the formula R = log I , where R is the measurement of the Richter scale and I is the intensity, to find the intensity of an earthquake with a Richter scale of 7.567 Round your answer to four decimal places.
What is 36,897,759.8570?
500

Solve

10^(2x+1) + 2 = 4

Round your answer to two decimal places.

x ≈ -0.35

500

Solve: Hint: two answers

What is x=4 and x = -4 ?

M
e
n
u