Solve for x 3(2^x)=42

Problem

3*(2)=42

Solution

1. Isolate the exponential term by dividing both sides of the equation by 3

2=42/3

2=14

2. Apply the natural logarithm to both sides of the equation to bring the variable down from the exponent.

ln(2)=ln(14)

3. Use the power rule of logarithms, which states ln(ab)=b*ln(a) to move the x in front.

x*ln(2)=ln(14)

4. Solve for x by dividing both sides by ln(2)

x=ln(14)/ln(2)

Final Answer

x=ln(14)/ln(2)

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