Exponents and Logs

Solving Exponential Functions

100

2^x = 2⁵

x=5

200

5^2x = 5²⁰

x = 10

300

3^3x = 9^2x-6

x = 12

400

4^x = 8^2x+5

x = 15/4 OR 3.75

500

16^x-5 = (1/32)^x-6

x = -5

Exponent to Log

100

8² = 64

log₈64 = 2

200

17² = 289

log₁₇289 = 2

300

256^1/2 = 16

log₂₅₆16 = 1/2

400

(1/6)³ = (1/216)

log_(1/6)(1/216) = 3

500

64^-1/2 = 1/8

log₆₄(1/8) = -1/2

Log to Exponent

100

log₂4 = 2

2² = 4

200

log₈64 = 2

8² = 64

300

log₅(1/25) = -2

5^-2 = 1/25

400

log_(1/8)64 = -2

(1/8)^-2 = 64

500

log100 = 2

10² = 100

Solving Logarithmic Functions

100

log₂x = log₂10

x = 10

200

log5x = log2x-9

x = -3

300

log(-5x-6) = log(x²)

x = -2

x = -3

400

log₂x-log₂10 = 2

x = 40

500

2log₅4+log₅x = 3

125/16 OR 7.8125

Common Logs

100

Given log3=5 and log2=3, what is log15?

log15= 5+3 = 8

200

Given log2=3 and log5=2, what is the value of log5/2?

log5/2= 3-2 = 1

300

Given log2=3 and log3=4, what is the value of log12?

log12 = (log2)(log2)(log3) = 3+3+4 = 10

400

Given log3=5, log2=3 and log5=7, what is the value of log(12/5)?

log(12/5) = (log2)(log2)(log3)/(log5) = 5+3+3-7 = 4

500

Given log2=5 and log3=2, is it possible to find the value of log42?

No