Question

Please assist me with this.​

Answer 1

Answer: Choice A)
`10^(-6)` watts per square meter

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Work Shown:

L = loudness of a sound

`L = 10\log\left((I)/(I_0)\right)\\\\60 = 10\log\left((I)/(10^(-12))\right)\\\\6 = \log\left((I)/(10^(-12))\right)\\\\6 = \log\left(I\right) - \log\left(10^(-12)\right)\\\\6 = \log\left(I\right) - (-12)\log\left(10\right)\\\\6 = \log\left(I\right) + 12\log\left(10\right)\\\\6 = \log\left(I\right) + 12*1\\\\6 = \log\left(I\right) + 12\\\\6-12 = \log\left(I\right)\\\\-6 = \log\left(I\right)\\\\\log\left(I\right) = -6\\\\I = 10^(-6)\\\\`

Answer 2

Answer: A) 10⁻⁶

Explanation:

`\text{Equation:}\ 10\ log\bigg((I)/(I_o)\bigg)=d\\\\\text{Given:}\ I_o=10^(-12),\ d=60\\\\\\10\ log\bigg((I)/(10^(-12))\bigg)=60\\\\\\.\quad log\bigg((I)/(10^(-12))\bigg)=6\qquad \text{(divided both sides by 10)}\\\\\\.\quad \qquad (I)/(10^(-12))=10^6\qquad \text{(used rules to eliminate log)}\\\\\\.\qquad \qquad I=10^6(10^(-12))\quad \text{(multiplied both sides by}\ 10^(-12))\\\\.\qquad \qquad I=10^(-6)\qquad \qquad \text{(simplified by adding exponents)}`

`\large\boxed{10^(-6)}`