Simple Logarithmic and Exponential Equations

Solve the equation for x.

• 22.198

• e

• 1.131

• 21.66

Rewrite log_pt = m in exponential form.

• p^t = m

• t^m = p

• m^t = p

• p^m = t

Write the exponential equation as a logarithm
6³=216

• log₆(3) = 216

• log₃(6) = 216

• log₆(216)=3

• log₂₁₆(6)=3

Evaluate log₅  20 to the third decimal place

• 0.537

• 2.996

• 1.301

• 1.861

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

• log₂(x/y⁵)

• log₂(xy⁵)

• log₂(x/y)⁵

• log₂(x/5y)

Write log_b(x/y) as two logs

• log_bx-log_by

• log_bx+log_by

• log_bx*log_by

• log_bx/log_by

log₆(2x + 3) = 3

• x = 106.5

• x = 100

• x = 16

• x = 50

log₅ (2x - 3)² = 6

• x = 128

•  x = 64

• x = 4

• x = 14

log x - log 8 = 3

• x = 1000

• x = 800

• x = 8000

• x = 100

log(x+6) = 1

• 4

• 4.222

• -5

• -9.550