Given that logJ025 K clearly show why logJ16 2KSolutionlog

Given that log_J(0.25) = K, clearly show why log_J(16) = -2K.

Solution

logJ(0.25) = K

Prove logJ(16) = -2K

logJ(0.25) = K

logJ(25/100) = K

logJ(1/4) = K

logJ(2^-2) = K

-2logJ(2) = K

logJ(2) = -K/2

Multiply both sides by 4

4logJ(2) = -2K

logJ(2^4) = -2K

logJ(16) = -2K