Converting Between Exponents and Logs

Write in logarithmic form:

a^b = c

• log _a c = b

• log _b c = a

• log _a b = c

• log _b a = c

Change to logarithmic form.

3^h = w

• log_w3 = h

• log₃w = h

• log_h3 = w

• log₃h = w

Convert 3^x = 12 to the equivalent log form.

• 3¹² = x

• log_x 3 = 12

• log₃ x = 12

• log₃ 12 = x

Change to exponential form.

log_a2 = 5

• a² = 5

• 5² = a

• a⁵ = 2

• 2⁵ = a

Rewrite each logarithmic equation as an exponential equation and vise versa

Mathematical Equivalence

ON

Rewrite each logarithmic equation as an exponential equation and vise versa

Mathematical Equivalence

ON

14² = 196

• log₁₄ 196 = 2

• log₂ 14 = 196

• log₂ 196 = 14

• log₁₄ 14 = 2

log₁₃169=2

• 2¹³ = 169

• 13² = 169

• 169² = 13

• 13¹⁶⁹ = 2

Change the logarithm to an exponent.

Mathematical Equivalence

ON

Write 6^x = 8 in log form.

• log₆ 8 = x

• log₈ 6 = x

• log₆ x = 8

• log₈ x = 6