Logs!
Exponential EQ's
Word Problems
Solving Exponential EQ's
Solving Log EQ's
Transformations
100
Simplify the expression:
log (base 2) 8
What is 3?
100
Write the exponential equation 4^5= 1,024 in logarithmic form.
What is log (base 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
Solve:
8^(2x)=8^(x+7)
What is x=7?
100
Solve:
log x = 3
What is 1000?
100
-12
200
Write the equation log (base 3) 729 = 6
in exponential form.
What is 3^6=729 ?
200
Write the exponential equation 27^ (1/3) = 3 in logarithmic form.
What is log (base 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? Round to the nearest whole number.
What is 3 hours?
200
Solve:
25^(x-4)=5^3x+1)
What is x=-9 ?
200
log (base 3) x = 5
What is x = 243 ?
200
If I wanted to transform the graph y=2x by reflecting the x-axis and shifting to the left 4, what would by equation be?
y=-2x+4
300
Write the equation log 1000 = 3 in exponential form.
What is 10^3=1000 ?
300
Write the exponential equation (1/2)^-3=8 in logarithmic form.
What is log (base 1/2) 8 = -3
300
Ryan invests a sum of money in a savings account with a fixed annual interest rate of 4.31% compounded 12 times per year. After 10 years, the balance reaches $12,855.94. What was the amount of the initial investment?
$10,253.04
300
Solve:
e^(2x)=e^(x+4)
What is x=4?
300
Solve:
ln x = 4
Round your answer to two decimal places.
What is x= 54.60 ?
300
Which function has a vertical asymptote?
Log
400
What is the asymptote of the graph of
f(x) = log(x - 1) ?
What is x=1 ?
400
Is the graph y= .7^x increasing or decreasing, and is it a function?
What is decreasing and yes, a function?
400
The formula shown relates the mass, M, in kilograms, to the length, L, in centimeters, of female spinner dolphins.
log M = 2.65(log L) - 4.22
According to the formula, what is the approximate mass of a female spinner dolphin that is 152.4 cm in length?
36.72 kg
400
Solve:
3e^(3 - x)= 15
Round your answer to two decimal places.
What is x= 1.39 ?
400
Solve:
3 ln x - 7 = 4
Round your answer to two decimal places.
What is x= 39.12 ?
400
Which equation has a horizontal asymptote?
Exponential
500
What is the asymptote of the graph of
f(x)= log(x + 2) -1 ?
What is x= -2 ?
500
Simplify ln e ^(3x)
What is 3x?
500
Given 450,000(1.091)m, what is the rate?
9.1%
500
Solve:
10^(2x+1) + 2 = 4
Round your answer to two decimal places.
What is x = -0.35 ?
500
Solve:
Hint: two answers
What is x=4 and x = -4 ?
500
Given
g(x)= -4x+2-8
f(x)= log(2x+2)+1
State the asymptotes for each.
g(x) - y=-8
f(x) - x=-2