Logarithms!

Natural logs and base e

100

Write equation in logarithmic form

e^x = 3

x = ln 3

200

Write equation in exponential form

ln 15 = x

e^x = 15

300

Simplify as a single logarithm

2 ln x + 2 ln 4

ln 16 x²

400

Solve equation and round to four decimal places

5e^x + 1 > 7

x > 0.1823

500

Write as a logarithmic function

e^5x + 4 > 34

x > ln 6

logs and properties of logs Category

100

Write equation in exponential form

log₉ 3 = 1/2

9^1/2 = 3

200

solve equation and round to four decimals

log₁₀ 4 + log₁₀ w = 2

w = 3.1622

300

Find x

log₂₇ 1/3 = x

x = -1/3

400

Find n

log₄ (n + 1) - log₄ (n - 2) = 1

n = 3

500

Find x

log₇ x + 2 log₇ x - log₇ 3 = log₇ 72

x = 6

solving exponential equations

100

Find x

25^{2x + 3} = 25^{5x - 9}

x = 4

200

Find x

9^{8x - 4} = 81^{3x + 6}

x = 8

300

Find x

4^{3x - 3} = 8^{4x - 4}

x = 1

400

Find x

(1/36)^{6x - 3} > 6^{3x - 9}

x > 1

500

Find x

64^{4x - 8} < 256^{2x + 6}

x < 12

graphing exponential functions

100

Exponential Functions equation (including the variables: a, b, h, and k)

f(x) = ab^x-h + k

200

h is what kind of translation

horizontal

300

If a < 0, the graph is reflected on what axis?

x-axis

400

k is for what kind of translations

vertical

500

If |a| > 1, the graph is _______ vertically.

(stretched or compressed?)

stretched

common logs

100

Use calculator! Round to three decimal places

log 9

= 0.954

200

Write in terms of common logarithms. Then simplify and round to four decimal places.

log₈24

log24/log8

= 1.5283

300

DOUBLE POINTS! (600)

208³ = 49^{x - 4}

x = 8.1144

400

Find x. Round to four decimal places

8^x > 9^{2x + 2}

x > -3.5642

500

Write as a single logarithm

log₂7/log₂3

log₃7