Logarithms Algebra 2

Properties

100

log_b (xy) = ___________

lob_bx + log_by

200

 A logarithm is a(n) _________________

exponent

300

log_b xⁿ = 

nlog_bx

400

Use the Change of Base to solve this logarithm. You are changing it to a base 10

log_3 56

(log_10 56)/(log_10 3) = 3.66

500

log 10^x

x

Evaluating Logs 1

100

 solve for x 

10^x = 3

0.477...

200

Solve for x

6^x = 152

2.803881...

300

Solve for x

3.5 x 10^x = 8.53

0.386...

400

Solve for x

7^3x = 10,000

1.577...

500

18 x 5^-0.3x = 0.007

16.262...

Evaluating logs 2

100

Solve for x

10^5x = 2500

0.679...

200

Solve for x

log₅0 = x

no solution

300

Solve for x

log_3 (1/9) = x

-2

400

Write as a single argument

log₂225 - log₂5 + log₂3

log₂135

500

0.7^3x = 21.9

-2.8845...

Inverse functions/Add-Multiply Property

100

The inverse of a function is obtained by ___________ the two ______________.

interchanging, variables

200

Find the inverse of f(x) = 0.2x + 3

f^-1 (x) = 5x - 15

300

Are f(x) = (x + 5) and g(x) =   1/(x + 5)  inverses of one another

no

400

f(x) varies exponentially with x. If f(3) = 100 and f(5) = 80, calculate the values of f(x) for two larger values of x and two smaller values of x.

f(-1) = 156.25   f(1) = 125    f(7) = 64   f(9) = 51.2

500

Is this an exponential function?

x =      5      10     15    20

f(x) =   20    40     60    80

No

Wild

100

What is the understood base of a log?

10

200

What does the word logarithm stand for?

logical algorithm

300

Rewrite this in log form   24^x = 13,824

log₂₄ 13,824 = x

400

Solve for x 

24^x = 13,824

x = 3

500

Explain why any number raised to the 0 power is equal to one. Use words and examples in your answer. 

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