Exponential and Log Solving

Expanding Logs: Use properties of logarithms to expand the given problem completely and choose the correct answer.

Solving Log Equations: Use Properties of logarithms to solve the given equation for the variable and choose the correct solution.

• 5

• 13

• 84

• -20

log (x - 1) - log (x - 2) = log 5

• 7

• 4/9

• 9/4

• 1/7

ln(x+8) - ln (8) = 3

• 152.68

• 188.77

• 4.24

• 8.01

Write log_b(x/y) as two logs

• log_bx-log_by

• log_bx+log_by

• log_bx*log_by

• log_bx/log_by

Use multiple log properties to write as a sum or difference of two logs: log(4x³) 

• log 4 + 3log x

• 3log 4 + 3log x

• 3log 4 + log x

• log 12 + log x

Use multiple log properties to write as a single log:
log₂x -  5log₂y

• log₂(x/y⁵)

• log₂(xy⁵)

• log₂(x/y)⁵

• log₂(x/5y)

Solve for x:  log₆x + log₆(x-5) = 2

• √7

• 9

• 4

• none of these

log₉(10)-log₉(x-3) =log₉(72)

• 81/16

• 113/36

• No Solution

• 92/15

log₉(x)+log₉(x+2)=log₉(35)

• 5

• -7

• 5, -7

• -7, -13