Converting Log and Exponential Form
Convert to Exponential Form:
log_2(8)=x
2^x=8
Solve for x:
log_x216=3
x=6
Condense the Logarithms:
log_3(2x)-log_3(5y)
log_3((2x)/(5y))
Solve using Logarithms:
log_7(49) = x
x=2
You invest $3400 into an account which compounds continuously at a rate of 3.2%. How much will be in the account after 8 years?
$4391.96
You purchase a new truck for $65,000. It depreciates at 15% per year. You plan to keep it for 10 years and then sell it. What will the value of the truck be after 10 years?
$12,796.84
Convert to Logarithmic Form:
4^y=x
log_4(x)=y
Solve for x:
log_3(x-3)=2
x=12
Completely Expand the Logarithm:
log((2x)/y)
log(2)+log(x)-log(y)
Solve Using Logarithms:
log_3(1/27)=x
x= -3
After 9 years at a rate of 6.5%, an account that compounds continuously has $11,757.19 in it. What was the initial deposit?
$6550
Bob the Builder built a big blue house. It appreciated at a constant rate of 20% per year. How much was the value initially if it was worth $540,000 after 14 years?
$42,058.75
Convert to Exponential Form:
log_(x-1)(4)=2y
(x-1)^(2y)=4
Solve for x:
log_4(2)+log_4(x+6)=1
x=-4
Condense the Logarithms:(use ln the same as any other log)
2log(3)+4log(y)-2log(x)
log((9y^4)/x^2)
Solve by Converting:
log_4(x)=-5
x=
x = 1/1024
You invest $7500 into an account which compounds monthly at a rate of 4.75%. How much will be in the account after 15 years?
$8,344.20
Wheel Warrior purchased a new ebike when they had a sale at Trailhead Cycle in Champlin for $5800. It depreciated at 12% per year. Wheel Warrior decided to trade it in and was surprised to find out it is only worth $2000. How long has he had the ebike?
8.329 years
Convert to Exponential Form:
log_(3x)(5-z)=4y
(3x)^(4y)=5-z
or
Solve for x:
4log_9(3)-log_9(x)=2
x=1
Condense the Logarithms:
3log(x)+3log(3)-(4log(2)+ 5log(z))
log((27x^3)/(16z^5))
Solve using Logarithms:
log_x(1/64) = -2
x = 8
How long will it take $45,000 to grow to $70,000 if it compounds quarterly at a rate of 3.6%.
15.6 years
Convert to Logarithmic Form:
10^(x+4)=2y-7
log(2y-7)=x+4
Solve for x:
log_2(8x)-3log_2(4)= 3
x=64
Completely Expand the Logarithm:
log((3x^6y^7)/(7z^5))
log(3)+6log(x)+7log(y)-(log7+5log(z))
Solve using Logarithms:
log_25(5)=x
x=1/2
How much more will you make at 7% than you make at 5% if you invest $1000 into an account that compounds continuously for 4 years?
$101.73