Exponential and Logarithmic Equations (3.4)

If log2=0.3010 and log5=0.6989

100

Find log (2/5)

-0.3979

200

Find log (10)

0.2104

300

Find log (4)

0.6021

400

Find log (50)

1.6990

500

Find log (80) 

1.9031

Change the Base and Apply

100

log₃ (2) =     to the nearest ten-thousandth

~ 0.6309

200

log₇ (4) =      to the nearest ten-thousandth

~ 0.7124

300

The pH of a solution is given by -log[H+] where H+ is the concentration of hydrogen ions.  Find the pH if

[H+] = 3.33 x 10⁴ to the nearest tenth.

pH = -4.5

400

The pH of a solution is given by 6log[H+] where H+ is the concentration of hydrogen ions.  Find the pH if

[H+] = 1.0 x 10^-5 to the nearest tenth.

pH = -30

500

The yield v (in millions of cubic feet per acre) for a forest at age t years is given by                                  v = 6.7 + log₂ (t/0.25). Find amount of acreage after 8 years.

v = 13.7 millions of cubic feet per acre

Basic Log Equations and their properties

100

True or False.

log (x/y³) = log x - 3 log y

True

200

log (ab) = log (a + b)

False

300

Solve for x algebraically. log x=-3

x = {0.001}

400

Solve for x algebraically. log₂ x -7=0

x = {128}

500

Solve for x algebraically.  Then, approximate your answer to three decimal places. 3log₄ (5x) =10

x ~ 20.319

Equations & Inequalities

100

Solve log(3x - 2) = 2

x = {34}

200

Solve log₂ (x + 4) = log₂ (5x - 8)

x = {3}

300

log₃ (2x + 4) = log₃ (x -10)

x = No Solution

400

Solve log₂ (x + 6) < log₂ (17)

{x| x < -6}

500

Solve log₃ (x-3)/4 + 5 > log₃ (x + 12)

{x| x < 17}

More Eqs/Ineqs

100

log₆ (2c) + log₆ (8) = log₆ (80)

c = {5}

200

log₂ (x + 4) - log₂ (x - 3) = 3

x = {4}

300

log₅ (x) + log₅ (3x-5) = log₅ (2)

x = {2}

400

Solve and round to the nearest ten-thousandths.

9^x-2 > 38

{x| x > 3.6555}

500

Solve and round to the nearest ten-thousandths.

2ⁿ⁺¹ <5^2n-1

{x| x < 0.9117}