Evaluate this problemwithout using a calculator

Question

log₈  ⁴√1/32768

 

If the answer is not an integer, enter it as a decimal in its simplest form

Answer 1

log₈ (1/32768)^1/4 =

 

1/4 log₈ (1/32768) =

 

-1/4 log₈ 32768 =

 

-1/4 log₈ 8⁵ =

-1/4 (5) = -5/4

Answer 2

log₈4√(1/32768) = log₈√(16/32768) = ½log₈(2048) = ½log₈(2048) = ½log₈(8³ *4) = ½log₈(8³) + ½log₈(4) = 3*½ log₈(8) + ½ log₈(64^?) = 3*½ + ? * ½ log₈(8²) = 3/2 + 2 * 2/6 + log₈(8) = 3/2 + 4/6 = 3/2 + ? = 9/6 + 4/3 = 13/3