Logarithms Practice

Evaluating

100

Write the following as an exponent: 

log₂(1/32)=-5

(2)^-5 = 1/32

200

What are the two special cases of  logarithms? 

1. log_b(b) = 1 for any b>0

2. log_b(1) = 0 for any b>0

300

What is log₃(-3) = ?

no solution

400

What is log₂(1/64) = ?

-6

500

What is log₃(81) = ?

4

Expanding

100

log₂(xy)

log₂(x)+log₂(y)

200

log₈(xy²z⁵)

log₈(x)+2log₈(y)+5log₈(z)

300

log₇(k/m³)

log₇(k)-3log₇(m)

400

log(9s)^(x+2)

(x+2)log(9)+(x+2)log(s)

500

log₅((xy)^2/z)^6

12log₅(x)+12log₅(y)-6log₅(z)

Condensing

100

log(m)-log(z)

log(m/z)

200

log₇(16)+log₇(y)-log₇(4)

log₇(4y)

300

7log₃(h)+3log₃(k)-2log₃(x)

log₃(h⁷k³/x²)

400

8log₆(m)+(log₆(x))/2

log₆(m⁸ (x)^(1/2) )

500

log₂(w) + (log₂(x))/2 + (log₂(y))/2 + (log₂(z))/2 

 log₂(w (xyz)^(1/2))

Solving Using Exponents

100

log₁₅n = log₁₅3n

no solution

200

log₄(-5p-5) = log₄(-3p+4)

p = -9/2

300

log(2)+log(x) = 2

x=50

400

log₇(8)-log₇(-5x) = log₇(38)

x = -4/95

500

log₃(4) + log₃(4 - x²) = log₃(12)

x = 1 and x = -1

Solving Using Logarithms

100

74 = 8^2x

x = 1.035

200

5^x-2 = 24

x = 3.975

300

8^-5a - 5 = 53

a = -0.391

400

3(6^2x) - 10 = 152

x = 0.225

500

2(3^x+2) - 10 = 32

x = 0.771