6.6
6.8
Converting Between Forms
Miscellaneous
100
Solve the equation.
log3x = 5
x = 243
100
What does the doubling time refer to?
The time it takes for a population to double.
100
Write logb(x)=y in exponential form.
by=x
100
What's the inverse of a logarithmic function?
Exponential function
200
Solve the equation.
log5(x + 3) = 1
x = 2
200
A(t)=50e0.06t
What is the initial population for this function?
50!
200
Write ax=y in logarithmic form.
loga(y)=x
200
What's the base of a common logarithm?
10
300
Solve the equation.
log (x + 5) = log (4x + 2)
x = 1
300
What formula can we use to model uninhibited growth (or decay?)
N(t)=N0ekt
300
Write e10=22026 in logarithmic form.
ln(22026)=10
300
What's the base of a natural log?
e
400
Solve the equation.
3x = 27
x = 3
400
If a population of bacteria increases at a rate (k) of 0.08 with time (t) in days, how long will it take for the population to double?
About 8.7 days
400
Write ln(4x)=y in exponential form.
ey=4x
400
What is the automatic base on a standard calculator when you press log?
10
500
Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places.
(9/8)2=61-x
x ≈ 0.938
500
Solve the problem.
The half-life of silicon-32 is 710 years. What is k or the rate for the exponential decay equation?
k= -9.76x10-4
Or
k=-0.000976
500
Write log2(x)=-f(x) in exponential form.
2-f(x)=x
500
What must logarithm bases always be?
A positive number