Solving Logarithmic and Exponential Equations

Logarithms with the Same Base

100

Solve:

log₇(2x)=log₇4

x=2

200

Solve

log₁₄(3x+3)=log₁₄15

x=4

300

Solve

log₃(7x-13)=log₃(8x+2)

-15=x

400

Solve

log₇₄(-3x+17)=log₇₄(4x-15)

32/7=x

500

Solve

log₃₆(16x+1000)=log₃₆(62x-580)

1580/40=x

Converting Logarithms to Exponents

100

Solve

log₂x=6

64=x

200

Solve

log_x9=2

x=3

300

Solve

log₂(x+4)=7

124=x

400

Solve

log₇(5x+8)=3

67=x

500

Solve

log₄(3x+9)=4

247/46=x

Converting Exponents to Logarithms

100

Solve. Round to the nearest hundredth.

3^x=24

x≈2.89

200

Solve. Round to the nearest hundredth.

9^-x=31

x≈-1.56

300

Solve. Round to the nearest tenth.

12^x= 112

x≈1.9

400

Solve. Round to the nearest hundredth.

132^x=12

x≈0.51

500

Solve. Round to the nearest hundredth.

102^-x=1340

x≈-1.56

Exponential Growth & Decay

100

Initial Value(a):100

Growth Factor(r):5%

Time Passed(x):7

Solve Using a(1+r)^x round to the nearest hundredth

y=140.71

200

Initial Value(a):230

Growth Factor(r):50%

Time Passed(x):8

Solve Using a(1+r)^x round to the nearest hundredth

y=5894.65

300

Initial Value(a):700

Decay Factor(r):60%

Time Passed(x):3

Solve Using a(1-r)^x

y=44.8

400

Lizzie loves burning down neighborhood houses.  If her neighborhood had 40,000 houses in 2010 and Lizzie continues to burn down houses annually by 6% how many homes will be left in 2017

y=25436

500

Kerrington has ownership of chain of Coffee shops that operated 10,310 esthabshilents across the world in the year 1999. If the rate of Coffee shops being built continues to rise  by 7% annually, how many Coffee shops will Kerrington  operate in 2016?

y=32567