Exponential Equation
Solve
4^(3x)=8^(x+1)
x = 1
Write in exponential form
log x = 35
10^35 = x
Expand the expression: log (5mn)
log 5 + log m + log n
f(x) = 2^x - 7
a) Identify the parent function.
b) Describe the transformations.
a) f(x) = 2x
b) down 7
What equation is used for compound interest?
A = P(1 + r/n)^(nt)
Solve
3^x = 25
Solve 3^x = 25x= 2.930
Solve
log_3(5x-1)=log_3(x+7)
x = 2
Condense the expression:
log 6+2*log 2 - log3
log 8
f(x) = -3(2)^(x-3) + 4
Identify the transformations.
- Reflected over x-axis
- Stretched by 3
- Right 3
- Up 4
Is the following equation exponential growth or decay?
f(x) = 2(1/3)^x-4
Decay
Solve
e^(5p-8)= 12
x = 2.0970
Solve
log_5(3x+1)=2
x = 8
Daily Double!!
Expand the expression:
log_9((2x^(3))/3)
log_9 2+3log_9x-1/2
Identify the Asymptote
f(x) = log_5(x-2)+1
x = 2
The current population of a town is 8,200. If the population increases by 15% each year, find the population of the town in 12 years.
43,872
Solve
4+3^(x+1)=8
x=0.262
Solve
ln 5x = 4
x = 10.9196
Condense the expression:
3lnx+ln4-lnx-ln6
ln ((2x^2)/3)
Identify the End Behavior
f(x) = log_(1/2)(x+9) + 4
x -> -9 , f(x)->\infty
x -> \infty, f(x)->-\infty
Maddie bought a new car in 2020 for $36,000. Each year, it will depreciate at the rate of 6.5%. What will the value of her car be in 2029?
$19,661.06
Solve
10^(2x-3) +4=21
x=2.12
Solve
log_2(x)+log_2(x-7)=3
x = 8
Expand the expression:
log sqrt(100x^4y^7)
1+ 2*logx + 7/2* logy
Identify the Domain, Range, and Asymptote:
f(x) = 2(1/4)^x-9
Domain: All Real Numbers
Range: y > -9
Asymptote: y = -9
Jason took out a $20,000 loan for college. If the interest on the loan is 7.5% compounded monthly, how much will he pay in total after 10 years?
$42,241.29