LG 6 Summary-Eve Tarpey

Exponential form to log form

100

2⁸=256

log₂(256)=8

200

56.2341=100^(7/8)

log₁₀₀(56.2341)=7/8

300

12⁰=1

log₁₂(1)=0

400

15¹=15

log₁₅(15)=1

500

0.001=100^-3/2

log₁₀₀(0.001)=-3/2

Log form to exponential form

100

log₄(64)=3

4³=64

200

log₁₈(1889568)=5

18⁵=1889568

300

log(0.1)=-1

10^-1=0.1

400

log_x(8)=y

x^y=8

500

log₁₀₀₀₀(x)=24

10000²⁴=x

solving equations for a variable

100

log x + log 15 = 90

log x + log 15 = 90

log (15x) = 90

x/15=90/15

x=5

200

log x + log 8 = 30

log x + log 8 = 30

log (8x) = 30

x/8 = 30/8

x=3.75

300

log (x+4) + log (5) = log (5x+20)

log (x+4) + log (5) = log (5x+20)

log (5x+20) = log (5x+20)

x = 1

400

log (6) - log (x) = log (1/2)

log (6) - log (x) = log (1/2)

log (6/x) = log (1/2)

x=12

500

log_a(64)- log_a(16) = log₄(16)

log_a(64)- log_a(16) = log₄(16)

64/16 = 4

log_a(4) = log₄(16)

a=2

equations with the same base

100

3^x=27

3 x 3 x 3 = 27

x=3

200

h^5x+2=h^x-6

5x+2 = x-6

x=-2

300

8^2x-2=8^x-1

2x-2=x-1

x=1

400

156^6x-3=156^12x+3

6x-3 = 12x +3

x=-0.5

500

b⁴b^6x-2=b²⁰

6x-2+4=20

x=3

equations with a different base

100

9^x=3^3x+2

9^x=3^3x+2

3^2x=3^3x+2

2x=3x+2

x=-2

200

25^x+2=5^4x+6

25^x+2=5^4x+6

5^2x+4=5^4x+6

2x+4=4x+6

x=-1

300

100^4x=10^8x

100^4x=10^8x

10^8x=10^8x

x=1

400

15625^x-1=25^9x

15625^x-1=25^9x

x=-0.5

500

1000^x=10^2x

1000^x=10^2x

4x=2x

x=0