Question

Hello!

Answer 1

Answer:

$T_0=80695.17162...$

Explanation:

Given equation:

$\ln \left(\dfrac{T_0-100}{T_0}\right)=-0.00124$

To solve the given equation:

$\textsf{Apply log rules}: \quad e^{\ln (x)}=x$

$\implies \dfrac{T_0-100}{T_0}=e^{-0.00124}$

Multiply both sides by T₀:

$\implies T_0-100=T_0e^{-0.00124}$

Add 100 to both sides:

$\implies T_0=T_0e^{-0.00124}+100$

Subtract $T_0e^{-0.00124}$ from both sides:

$\implies T_0-T_0e^{-0.00124}=100$

Factor out the common term T₀:

$\implies T_0(1-e^{-0.00124})=100$

Divide both sides by $(1-e^{-0.00124})$

$\implies T_0=\dfrac{100}{1-e^{-0.00124}}$

Carry out the calculation:

$\implies T_0=\dfrac{100}{1-0.99876...}$

$\implies T_0=\dfrac{100}{0.001239231...}$

$\implies T_0=80695.17162...$