To determine

To find: We have to solve the equation e7-4x=6 for x.

Answer

The solution of the equation is  x=14(7-ln⁡x).

Explanation

Calculation:

First, we take the natural logarithms of both sides of the equation e7-4x=6. Thus

ln⁡e7-4x=ln⁡6,

 Since we know that

ln⁡ex=x (1)

Thus, using equation (1), we have

(7-4x)=ln⁡6

Or 4x=7-ln⁡6,

x=14(7-ln⁡x)

Conclusion:

The solution of the equation is  x=14(7-ln⁡x).

To determine

To find: We have to solve the equation ln⁡3x-10=2  for x.

Answer

The solution of the equation is x=13(10+e2).

Explanation

Calculation:

First, we are applying the exponential function on both sides of the equation

ln⁡3x-10=2. Thus

eln⁡(3x-10)=e2

Since we know that

eln⁡x=x (1)

Thus, using equation (1), we have

3x-10=e2

Or 3x=10+e2,

x=13(10+e2).

Conclusion:

The solution of the equation is x=13(10+e2).