Solve for x 8(3^(6-x))=40

Problem

8*(3(6−x))=40

Solution

1. Isolate the exponential term by dividing both sides of the equation by 8

3(6−x)=40/8

3(6−x)=5

2. Apply the logarithm to both sides to move the variable out of the exponent. We will use the natural logarithm ln()

ln(3(6−x))=ln(5)

3. Use the power rule of logarithms, which states ln(ab)=b*ln(a) to bring down the exponent.

(6−x)*ln(3)=ln(5)

4. Distribute the ln(3) or divide both sides by ln(3) to isolate the term containing x

6−x=ln(5)/ln(3)

5. Solve for x by subtracting 6 from both sides and then multiplying by −1

−x=ln(5)/ln(3)−6

x=6−ln(5)/ln(3)

Final Answer

x=6−ln(5)/ln(3)

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