this link will help you
www.algebra.com/algebra/homework/Exponential-and-logarithmic-functions/Exponential-and-logarithmic-functions.faq.question.189330.html
www.algebra.com/algebra/homework/Exponential-and-logarithmic-functions/Exponential-and-logarithmic-functions.faq.question.189330.html
V=10log(I/10^-16)
V=10log(10^-5/10^-16)
= 10log(10^11)
= 11(10log 10)
= 11(10)(1) = 110 decibels
Given: I = 10^-5 watts per centimeter
Substituting the value of I into the formula:
V = 10log(10^-5/10^-16)
To simplify the expression, we can use the property of logarithms: log(a/b) = log(a) - log(b).
V = 10(log(10^-5) - log(10^-16))
Using the property log(a^b) = b*log(a), we can further simplify:
V = 10(-5 * log(10) - (-16 * log(10)))
Since log(10) equals 1, the expression becomes:
V = 10(-5 - (-16))
Simplifying the exponent:
V = 10(-5 + 16)
V = 10^11
Therefore, the level of sound of loud music is 11 decibels.
Given:
Intensity (I) = 10^-5 watts per centimeter
Formula:
V = 10log(I/10^-16)
Substituting the given intensity into the formula:
V = 10log(10^-5/10^-16)
To simplify the calculation, we can simplify the fraction inside the logarithm:
V = 10log(10^11)
Using the logarithmic property log(b^a) = a * log(b):
V = 10 * 11
Calculating the final answer:
V = 110 decibels
Therefore, the level of sound of loud music is 110 decibels.