Answer
(a) $20\ dB$
(b) $30\ dB$
(c) $50\ dB$
(d) $60\ dB$
(e) $3\ dB$
Work Step by Step
Following the definition of Decibel Levels, we have:
(a) $d=10\ log(\frac{I}{I_0})=10\ log(\frac{100I_0}{I_0})=10\ log(100)=20\ dB$
(b) $d=10\ log(\frac{I}{I_0})=10\ log(\frac{1000I_0}{I_0})=10\ log(1000)=30\ dB$
(c) $d=10\ log(\frac{I}{I_0})=10\ log(\frac{100000I_0}{I_0})=10\ log(100000)=50\ dB$
(d) $d=10\ log(\frac{I}{I_0})=10\ log(\frac{1000000I_0}{I_0})=10\ log(1000000)=60\ dB$
(e) $\Delta d=10\ log(I_2)-10\ log(I_1)=10\ log(\frac{I_2}{I_1})=10\ log(2)\approx3\ dB$
