Converting Log and Exponential Form
Convert to Exponential Form:
log_2(8)=x
2^x=8
Solve for x:
5^(2x)=25
x=1
Condense the Logarithms:
log_3(2x)-log_3(5y)
log_3((2x)/(5y))
Solve using Logarithms:
log_7(49) = x
x=2
The half-life of Zn-71 is 2.4 minutes. If one had 100.0 g at the beginning, how many grams would be left after 7 minutes had elapsed?
A=A_0(1/2)^(h/t)
13.2g
Convert to Logarithmic Form:
4^y=x
log_4(x)=y
Solve for x:
5*2^x=240
log_(2)(48)
Completely Expand the Logarithm:
log((2x)/y)
log(2)+log(x)-log(y)
Solve Using Logarithms:
log_3(1/27)=
x= -3
If Phillip J. Fry left .93 in an account with 2.25% interest compounded yearly, how much would be in the account after 1000 years?
A=P(1+r/n)^(nt)
$4,283,508,450
Convert to Exponential Form:
log_(x)(4)=2y
(x)^(2y)=4
Solve for x:
3^(2x)=27
x=3/2
Condense the Logarithms:(use ln the same as any other log)
2log(3)-2log(x)+4log(y)
log((9y^4)/x^2)
Solve by Converting:
log_4(x)=-5
x = 1/1024
The half-life of Zn-71 is 2.4 minutes. If one had 100.0 g at the beginning, how long would it take for 30g to be left?
A=A_0(1/2)^(h/t)
4.2 minutes
Convert to Logarithmic Form:
2^(x+4)=y
log_2(y)=x+4
Solve for x:
2*3^(x-5)=12
log_(3)(6)+5
Condense the Logarithms:
3log(x)+4log(2)-5log(z)-3log(3)
log((16x^3)/(27z^5))
log((2^4x^3)/(3^3z^5))
Solve using Logarithms:
log_x(1/64) = -2
x = 8
If you put $200 in an account that continuously compounds at 3%, how long would it take for the amount to triple to the nearest year?
A=Pe^(rt)
37 years (36.6)
Convert to Exponential Form:
log_(3)(5-z)=4y
(3)^(4y)=5-z
Solve for x:
2^(3x)-7=13
(log_(2)(20))/3
Completely Expand the Logarithm:
log_7((3x^6y^7)/(z^5))
log_7(3)+6log_7(x)+7log_7(y)-5log_7(z)
Solve using Logarithms:
log_(x+2)(16)=2
x=2
A radioactive isotope lost 72% of its mass in 3 years. What is the half-life of the isotope?
1.63 years