Converting Exponents to Logs

Change to Logarithmic Form:
5³ = 125

• log ₅ 125 = 3

• log ₃ 125 = 5

• log ₅ 3 =125

• log₁₂₅ 3 = 5

Rewrite log₃t = 5 in exponential form.

• 5^t=3

• log₃5 = log₃t

• t⁵=3

• 3⁵=t

Rewrite log_vn = a in exponential form.

• v^a = n

• n^a = v

• vⁿ = a

• aⁿ = v

Change to exponential form.

log_a2 = 5

• a² = 5

• 5² = a

• a⁵ = 2

• 2⁵ = a

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81

• log₈₁3 = 4

• log₃81 = 4

• log₄81 = 3

log_nm= -2

• n^-2 = m

• m^-2 = n

• -2ⁿ = m

• mⁿ = -2

14² = 196

• log₁₄ 196 = 2

• log₂ 14 = 196

• log₂ 196 = 14

• log₁₄ 14 = 2

n^m = 156

• log_n 156 = m

• log_n m = 156

• log_m 156 = n

• log_n 16 = n

• log(x) + log(z) + 4log(y)
• 3log(x) − log(z) − 4log(y)
• 3log(x) + log(z) + 4log(y)
• log(x) − 4log(z) − 3log(y)

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

• log₂(x/y⁵)

• log₂(xy⁵)

• log₂(x/y)⁵

• log₂(x/5y)