Question

Solve the equation to find x:
7-3e^x=4

Answer 1

x = 0

Explanation:

Given equation:

`7-3e^x=4`

Add 3eˣ to both sides of the equation:

`\implies 7-3e^x+3e^x=4+3e^x`

`\implies 7=4+3e^x`

Subtract 4 from both sides of the equation:

`\implies 7-4=4+3e^x-4`

`\implies 3=3e^x`

Switch sides:

`\implies 3e^x=3`

Divide both sides by 3:

`\implies (3e^x)/(3)=(3)/(3)`

`\implies e^x=1`

Take natural logs of both sides:

`\implies \ln e^x=\ln 1`

`\textsf{Apply the natural log power law:} \quad \ln x^n=n \ln x`

`\implies x\ln e=\ln 1`

As ln e = 1 and ln 1 = 0:

`\implies x \cdot 1=0`

`\implies x =0`

Therefore, the value of x is x = 0.