An Open and Shut Base
2^(x+1)=4^(2x-1)
1
2log_6 4x=0
1/4
1/3log_2x+5=7
64
A radioactive substance with a mass of 320 grams decays 16% each year. What is the mass of the substance after 4 years?
Please round to nearest tenths.
159.3
3^(2x)= 11
Round to the nearest thousandths
1.091
8^(3x)=32
5/9
2log_4x=5
32
log_2x+log_2 3=3
8/3
Jorge invests $3000 today. They hope to double their money in 5 years. What annual interest rate would Jorge have to earn on their investment to reach their goal?
Round to the nearest tenth percent.
14.9%
If 3^(x+y)=9 and 3^(x-y)=9 then what is the value of x?
x=2
(1/9)^(2x) = 3^(7x-1)
1/11 or .091
-3-log_4(3x-8)=-4
4
5^logx=10^log5
x=10
If Jackie invests $2,000 in a certain bond that pays 8.25% interest compounded annually and Zazie invests $1800 in another bond that earn 10.3% annually, in how many years will their investments be equal in value? (Round to nearest tenth of a year)
5.6
2*3^(x/4)=5*7^(1-x)
1.289
5^(4x)*5^(2x-1)=5^(3x+11)
4
log_(x-1)3=1/2
10
log_5(x+1)-log_5(x-1)=2
13/12 or 1.083
Round to the nearest kilogram.
54 kg
3*3^x+3/3^x=10
x = -1, 1
64^(n-2)*(1/16)^(-n)=(1/4)^(3n+1)
5/8
log_3x=1+log_x9
9 and 1/3
x^(log_10 x)=100x
1/10 or 0.1 and 100
Jun buys a car that depreciates 12.5% annually. If they bought the car new for $15,000 and it is now worth $9,210, how old is the car?
Round to the nearest tenth of a year.
3.7 years
Find the sum of all integer solutions to the equation:
(x^2-3x+1)^(x+1)=1
3