Logarithms
log2 (5x + 7) = 5
x=5
62x=61-3x
x=1/5
If there are 3000 people at a protest, and the number of people increases by 25% each hour, how many people will there be in five hours? Round to the nearest whole number.
9155 people
Solve: 82x=8x+7
x=7
Solve logx=3
x=1000
log3 (9x + 2) = 4
x=79/9
23x=10
x=1/3log2
Use the formula R = log I , where R is the measurement of the Richter scale and I is the intensity, to find the Richter scale measurement of an earthquake with intensity 30,000,000. Round your answer to three decimal places.
7.477
Solve: e2x=ex+4
x=4
Solve: ln x = 4
x=54.60
log4 x + log4 (x -12) = 3
x=16
51-x=25
x=-1
Mr. and Mrs. Mitchell are saving for their daughter’s college education. They invest $10,000 in an account that pays 4.5% interest compounded continuously with the goal to have twice that amount in the account in ten year. Will the Mitchell’s reach their investment goal in ten years?
No
Solve: 25x-4=53x+1
x=-9
log3x = 5
x=243
log4 (2x +1) = log4 (x + 2) - log4 3
no solution
74-x=74x
x=4/5
If a $100 deposit is made at a bank that pays 12% per year, compounded annually, determine how long it will take for the investment to reach $2000.
26.4 years
Solve: 3e3-x= 15
x=1.39
Solve: 3 ln x - 7 = 4
x=39.12
log2 (x +1) - log2 (x - 4) = 3
x=33/7
8x²=83x+10
x=-2,x=5
Kelly invests $5000 with a bank. The value of her investment can be determined using the formula 𝑦 = 5000(1.06) 𝑡 , where 𝑦 is the value of the invesetment at time 𝑡, in years. Approximately how many years will it take for Kelly’s investment to reach $20 000?
23.8 years
Solve: 102x+1 + 2 = 4
x=-.35
log2(x+2)+log2(3)=log2(27)
x=7