Log a Rhythm and Exponentially Dance

Exponential Equations

100

-3e^9x-1 + 6 = -58; Solve for X. 

x=0.451 

200

Ms. Velasquez's lumber company has 1,200,00 trees. She plants plans to harvest 7% of the trees each year. How many years will it take Ernesto's company to harvest 750,000 trees. (Write the exponential equation and solve). 

Exponential Equation:

y=1,200,000(0.93)^X

Number years: 6.5 years

300

     Is the graph a Growth or Decay?

Decay

400

-6e^8x+8 -3 = -23; Solve for X. 

x = 0.8496

Conversion problems

100

Write 7⁵=16807 in logarithmic form

log₇16807=5

200

Write (1/3)²=9 in logarithmic form.

log_1/39=2

300

Write log₂32=5 in exponential form.

2⁵=32

400

Write log_1/51/625=4 in exponential form.

(1/5)⁴=1/625

Condensing/Expanding

100

Condense the logarithm; log₆ x + log₆y + 6log₆ z

log₆ (xyz⁶)

200

Condense the Logarithm; 2log₅(x)+ 12log₅(y)

log₅ (x² y¹²)

300

Expand; log₇ (2³/5²)

3log₇(2) - 2log₇(5)

400

Expand; log₅ (a³/b³)

3log₅(a) - 3log₅(b)

Logarithmic Equations

100

8^3x=32; Solve for X.

x=5/9

200

log_2x144=2; Solve for x.

x=6

300

log₄(x+3) + log₄(x+3) = log₄(49); Solve for x.

x=4

400

2 ln (x+7 )= 2.7; Solve for x. 

x=-3.14257