Logs!
Exponential EQ's
Word Problems
Solving Exponential EQ's
Potpourri
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?

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 3500 bacteria in a culture, and the number of bacteria increase by 25% continuously each hour, how much bacteria will be present after 2 hours?

What is 5770.5 

200

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


Hint: Rewrite 25 using a base of 5

What is x=-9 ?

200

log (base 3) x = 5

What is x = 243 ?

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

The expression  2e.3t  models the balance, in millions, where t represents time in months after the account was opened. What does .3 mean in context?

The account has a 30 percent continuous growth rate per month 

300

Solve: e^(2x)=50

What is approximately 1.96?

300

Solve: ln x = 4 Round your answer to two decimal places.

What is x= 54.60 ?

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 expression  2e.3t  models the balance, in millions, where t represents time in months after the account was opened. In which month will the account balance be 8,963,378.14 

What is 5 months 

400

Solve: 4(3)x=1/3

What is x is approximately equal to -2.26?

400

If given the graph of log10(x), explain why the coordinate (10000, 4) would be on the graph 

What is because 104=10000

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

Technetium-99m is used as a radioactive tracer for certain medical tests. It has a half-life of 1 day. Consider the function  where  T(d)=100(2)-d  is the percent of Technetium-99m remaining  days after the test. Which expression represents the number of days until only 2% remains?

-log2(1/5000)

500
Solve: 10^(2x+1) + 2 = 4 Round your answer to two decimal places.
What is x = -0.35 ?
500

How many more school days are left until summer break? 

What is 15

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