MT 2 LT 1 Properties of Logarithms Review

Logs

100

Rewrite the following exponential in logarithmic form. 

c⁶ = 8

log_c8=6

200

Rewrite the following exponential in logarithmic form. 

2^b = 9

log₂9 = b

300

Rewrite the following exponential in logarithmic form. 

10^y = h

log h = y

400

Rewrite the following exponential in logarithmic form. 

e⁵ = 7

ln 7 = 5

500

Rewrite the following exponential in logarithmic form. 

(1/2)^x = 14

log_1/2(14) = x

Exponentials

100

Rewrite the following logarithm in exponential form.

 log_v8 = a

v^a = 8

200

Rewrite the following logarithm in exponential form. 

log_b5 = 3

b³ = 5

300

Rewrite the following logarithm in exponential form. 

log7 = c

10^c = 7

400

Rewrite the following logarithm in exponential form. 

ln(x) = 3

e³ = x

500

Rewrite the following logarithm in exponential form. 

log_1/3(x+2) = 4

(1/3)⁴ = (x+2)

Evaluating Logs

100

log₂32

5

200

log₃(1/27)

-3

300

log base 7 of the third root of 49

2/3

400

natural log of one divided by the 7th root of e to the 4 power.  

-4/7

500

common log of the square root of 1000

3/2

Expanding Logs

100

log₃(x²y)

2log₃x + log₃y

200

log(x^a/y⁵)

alogx - 5logy

300

log₄[(x+2)/(16a⁵)]

log₄(x+2) - 2 - 5log₄a

400

natural log of the cube root of x times y to the 5th divided by z to the 3rd

(1/3)lnx + 5lny - 3lnz

500

log₃(x^a+7/81)

(a+7)log₃x - 4

Condensing Logs

100

3log₂a + 2log₂b

log₂(a³b²)

200

(1/2)ln x - 5ln y

ln(x^1/2/y⁵)

300

5log₃a + (3/2)log₃b - 4log₃c

log₃(a⁵b^3/2/c⁴)

400

log a - 2log b - 6log c

log(a/b²c⁶)

500

3log₄x - 5log₄y + 2log₄z

log₄(x³z²/y⁵)