the intensity, or loudness, of a sound can be measured in decibels (db), according to the equation…

the intensity, or loudness, of a sound can be measured in decibels (db), according to the equation (i(db)=10logleft\frac{i}{i_0}\right), where (i) is the intensity of a given sound and (i_0) is the threshold of hearing intensity. what is the intensity, in decibels, (i(db)), when (i = 10^{8}(i_0))?\n8\n9\n19\n80

the intensity, or loudness, of a sound can be measured in decibels (db), according to the equation (i(db)=10logleft\frac{i}{i_0}\right), where (i) is the intensity of a given sound and (i_0) is the threshold of hearing intensity. what is the intensity, in decibels, (i(db)), when (i = 10^{8}(i_0))?\n8\n9\n19\n80

Answer

Explanation:

Step1: Substitute $I = 10^{8}I_0$ into the formula

$I(dB)=10\log\left[\frac{I}{I_0}\right]=10\log\left[\frac{10^{8}I_0}{I_0}\right]$

Step2: Simplify the fraction inside the logarithm

$\frac{10^{8}I_0}{I_0}=10^{8}$, so $I(dB)=10\log(10^{8})$

Step3: Use the logarithm property $\log(a^{b}) = b\log(a)$

Since $\log(10^{8}) = 8\log(10)$ and $\log(10)=1$, then $I(dB)=10\times8\times1$

Step4: Calculate the final result

$10\times8\times1 = 80$

Answer:

80