Properties of Logs
Which property would you use to combine these logs?
log100 - log10
Quotient
Expand the log expression
log362
2log36
Condense the following logs
log_2(10)-log_2(5)
log_2(2)=1
Solve for x. Round to the nearest hundredth.
2^x=20
x=4.32
Solve for x
log_4(x)+log_4(2)=3
x=32
Which property would you use to combine these logs?
log25 + log24
Product
Expand the log expression
log_5(2/x)^4
4log_5(2)-4log_5(x)
Condense the following logs
3log_3(x)-2log_3(y)
log_3(x^3/y^2)
Solve for x. Give the exact answer.
3^(x-2)=9
x = 4
Solve for x
3log_2(x)-log_2(4)=log_2(16)
x = 4
Which property of logs would you use first to combine these logs?
2log4x - log4y
Power
Expand the log expression
log_9((x^2)/(2y^3))
2log_9(x)-log_9(2)-3log_9(y)
Condense the following logs
2log3-log3-4logx
log(3/x^4)
Solve for x. Round to the nearest hundredth.
e^(2x+3)=5
x = -0.70
Solve for x. Round to the nearest hundredth.
ln(x+2)-ln4=3
x = 78.34
Evaluate the following and identify the rule used. (round to the nearest hundredth)
log_3(5)
1.46
Change of base formula
Expand the log expression
logsqrt(x^3y^5)
3/2logx+5/2logy
Condense the following logs
1/3log_4(8)-5log_4(2)
log_4(1/16)
The population of lionfish in the waters surrounding Florida can be measured using the equation below where x is the number of years and y is the population in thousands? About how many years will it take for the population to reach 400,000?
y=250(1.04)^x
12 years
Solve for x.
log_9(x)+log_9(x-6)=1
No solutions
E.S. -3
You invest $100 into an account with an annual interest rate of 5.5% with continuous compounding. How long will it take for your investment to triple?
Hint: What is the equation you want to use?
A = Pe^(rt)
300 = 100e^(0.055r)
r ≈ 20 years