Exponentials and Logs

Log form

100

Write 13^x=y in log form

log₁₃y=x

200

Write 3^-2=1/9 in log form

log₃1/9=-2

300

Write 7^2x=12 in log form

log₇12=2x

400

Write (3x)^-5=y in log form

log_(3x)y=-5

500

Write 3y=5^(x/2) in log form

log₅ (3y)=x/2

exponential form

100

Write log₃9 = x in exponential form

3^x = 9

200

Write log_x 5 = 8 in exponential form

x⁸ =5

300

Write log_nm=-2 in exponential form

n^-2=m

400

Write log₃x = y in exponential form

3^y = x

500

Write log₈₁3 = 1/4 in exponential form

81^1/4 = 3

Log as inverse

100

Find the inverse function of y = 5^x

y = log₅x

200

Find the inverse function of y = log₂x

y = 2^x

300

Find the inverse function of y = 3^2x

y = 1/2log₃x

400

Find the inverse function of y = log₄ (x+5)

y = 4^x - 5 

500

Find the inverse function of y = 2^x/3 + 1

y = 3log₂(x-1)

Evaluate

100

log₈1

0

200

log₁₂12

1

300

log₅ 625

4

400

log₂ (1/32)

-5

500

log₃₆ 6

1/2

Solve

100

Solve for x    3^x = 7

x = 1.7712

200

Solve for x   log₃ (x-5) = 9

x = 19688

300

Solve for x   e^{(4x - 1)}= 3

x = 0.5247

400

Solve for t   3200 = 1600e^0.08t

t = 8.6643

500

A house was valued at $20,000 in 1950. At what rate is the value increasing if the house is worth $225,000 in 2022?

3.42%