Exponential & Logarithmic Equations

An Open and Shut Base

100

2^(x+1)=4^(2x-1)

1

200

8^(3x)=32

5/9

300

(1/9)^(2x) = 3^(7x-1)

1/11 or .091

400

5^(4x)*5^(2x-1)=5^(3x+11)

4

500

64^(n-2)*(1/16)^(-n)=(1/4)^(3n+1)

5/8

Teach an Old Log New Tricks

100

2log_6 4x=0

1/4

200

2log_4x=5

32

300

-3-log_4(3x-8)=-4

4

400

log_(x-1)3=1/2

10

500

log_3x=1+log_x9

9 and 1/3

Top Log

100

1/3log_2x+5=7

64

200

log_2x+log_2 3=3

8/3

300

5^logx=10^log5

x=10

400

log_5(x+1)-log_5(x-1)=2

13/12 or 1.083

500

x^(log_10 x)=100x

1/10 or 0.1 and 100

Rise To The Equation

100

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

200

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%

300

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

400

A radioactive substance decays at a rate of 0.6% per year.  In 13 years, there is 50 kg of the substance.  How many kg grams were there initially? 

Round to the nearest kilogram.

54 kg

500

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

Exponential Crisis

100

3^(2x)= 11

Round to the nearest thousandths

1.091

200

If  3^(x+y)=9 and  3^(x-y)=9  then what is the value of x?

x=2

300

2*3^(x/4)=5*7^(1-x)

1.289

400

3*3^x+3/3^x=10

x = -1, 1

500

Find the sum of all integer solutions to the equation:

(x^2-3x+1)^(x+1)=1

3