Converting Log and Exponential Form
Convert to Exponential Form:
log_2(8)=x
2^x=8
Estimate:
log221
4.39
Condense the Logarithms:
log_3(2x)-log_3(5y)
log_3((2x)/(5y))
Solve using Logarithms:
log_7(2x) = log_7(x+3)
x=3
Solve the equation with common bases:
3^(2x)=27
x=3/2
Convert to Logarithmic Form:
4^y=x
log_4(x)=y
Is the function exponential growth or decay?
y=3(2.5)x
Exponential Growth
Completely Expand the Logarithm:
log((2x)/y)
log(2)+log(x)-log(y)
Solve Using Logarithms:
log_3(1/27)=x
x= -3
Solve the equation using common bases:
3^(x+2)=27^(2x)
x=2/5
Convert to Exponential Form:
log_(x-1)(4)=2y
(x-1)^(2y)=4
Estimate:
log37
Between 1 and 2
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)=-3
x=
x = 1/64
Solve the equation using logarithm. Round to the hundredths place.
4^x=19
x=2.12
Convert to Exponential Form:
log_(3x)(5-z)=4y
(3x)^(4y)=5-z
or
Everleigh won $2,500 and deposited it into a savings account earning 4.2% interest compounded annually. How much was in the account after 10 years?
$3,772.40
Condense the Logarithms:
3log(x)+3log(3)-(4log(2)+ 5log(z))
log((27x^3)/(16z^5))
Solve using Logarithms:
log(x+1) = 2
x = 99
Solve the equation. Round to the tenths place.
2^(3x-4)=5
x=2.1
Convert to Logarithmic Form:
10^(x+4)=2y-7
log(2y-7)=x+4
Suppose you invest $3000 at an annual interest rate of 7.68%.How much money will be in the account after 15 years compounded semi-annually?
$9,290.98
Completely Expand the Logarithm:
log((3x^6y^7)/(7z^5))
log(3)+6log(x)+7log(y)-(log7+5log(z))
Solve using Logarithms:
log(5)-log(2x)=1
x=1/4
Solve the equation. Round to the hundredths place.
6^(2x)-2=8
x=0.64