Logarithmic & Exponential Equations
Write the log equation as an exponential equation:
log(2)=4x
What is ... 104x=2?
Condense the logarithm:
k log a+ g log d
What is ... log akd9?
Identify if the function is growth/decay & write the percentage:
y=260(1.692)x
What is ... growth & 69.2%?
Solve:
x2+3x+2=0
What is ... x=-1 & x=-2?
Luke invested $4,900 in an account paying an interest rate of 2.7% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 6 years?
What is ... A≈5800?
Write the log equation as an exponential equation:
log(5)=2x-5
What is ... 102x-5=5
Condense the logarithm:
7 log a - x log d
What is ... log a7/dx?
Identify if the function is growth/decay & write the percentage:
y=3900(0.954)x
What is ... decay & 4.6%?
Solve:
x2-10=3x
What is ... x=5 & x=-2?
Elijah invested $830 in an account paying an interest rate of 4.9% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 13 years?
What is ... A≈1563.30?
Solve for a positive value of x:
log(5)=2x-5
What is ... x=64?
Expand the logarithm;
log x2y4
What is ... 2 log x + 4 log y?
Identify if the function is growth/decay & write the percentage:
y=80(0.93)x
What is ... decay & 7%?
Solve:
3sin2θ+4sinθ=0
What is ... θ=0 & θ=π?
Peyton is going to invest in an account paying an interest rate of 4.7% compounded monthly. How much would Peyton need to invest, to the nearest ten dollars, for the value of the account to reach $460 in 20 years?
What is ... P≈180?
Solve for x, rounding to the nearest hundredth:
24x=30
What is ... x≈1.23?
Solve for the exact value of x:
log7(8x)+2log7(8)=2
What is ... x= 49/512?
A town has a population of 14000 and grows at 3% every year. What will be the population after 14 years, to the nearest whole number?
What is ... y≈21176?
Connor leans a 18-foot ladder against a wall so that it forms an angle of 70 degrees∘ with the ground. What’s the horizontal distance between the base of the ladder and the bottom of the wall? Round your answer to the nearest tenth of a foot if necessary.
What is ... 6.2 ft?
Ariana invested $90,000 in an account paying an interest rate of 1.5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $113,000?
What is ... t≈15.2?
Solve for x, rounding to the nearest hundredth:
3x=58
What is ... x≈3.7?
Solve for the exact value of x:
log2(8x)-3log2(6)=0
What is ... x=27?
An element with mass 490 grams decays by 18.8% per minute. How much of the element is remaining after 8 minutes, to the nearest 10th of a gram?
What is ... y≈92.6?
Nathan leans a 22-foot ladder against a wall so that it forms an angle of 76 degrees∘ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
What is ... 21.35 ft?
Alexa invested $630 in an account paying an interest rate of 5.5% compounded quarterly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $1,740?
What is ... t≈18.6?