Solve for x 5(2^(3-x))-13=100

Problem

5*(2(3−x))−13=100

Solution

1. Isolate the term containing the exponent by adding 13 to both sides of the equation.

5*(2(3−x))=113

2. Divide both sides by 5 to further isolate the exponential expression.

2(3−x)=113/5

3. Apply the natural logarithm to both sides to move the variable out of the exponent.

ln(2(3−x))=ln(113/5)

4. Use the power rule of logarithms to bring the exponent down as a multiplier.

(3−x)*ln(2)=ln(113/5)

5. Divide by ln(2) to isolate the linear expression containing x

3−x=ln(113/5)/ln(2)

6. Solve for x by subtracting 3 and multiplying by −1

x=3−ln(113/5)/ln(2)

Final Answer

x=3−ln(22.6)/ln(2)

Want more problems? Check here!