Logs and Exponentials

Log Problems

100

Write the following in exponential form

log₃27 = 3

3³ = 27

200

Find x (no need to simplify your logs)

5^x = 14

x = log14/log5

or

x = 1.64 (approximate)

300

Find x (no need to simplify your logs if any)

3^4x-5 = 38

x = (log38/log3 + 5)/4

or

x = 2.078

Log Laws

100

Simplify to a single logarithm

log₃28 - log₃7

log₃(28/7) or log₃4

200

Simplify the following (you don't need to get the actual value)

1/3 * log₇8

log₇2

300

Solve for x

ln(x) + ln(x-3) = ln(7x)

x = 10

Mystery Stuff

100

Graph log(x)

Lets hop over to desmos!

(turns out I have to pay money to have the image here sorry)

200

What is log(³√ 19)? 

1/3 log 19

or about 0.43

300

Scientists have found that the length in inches of a certain species of electric eel can be found by L = 22.4 ln(w) – 28.7, where w is the eel’s weight in pounds.

Find the weight of an eel that is 4 feet long round to the nearest tenth of a pound

30.7 pounds