Solve for x 3^(x+2)=20

Problem

3(x+2)=20

Solution

1. Apply the logarithm to both sides of the equation to isolate the exponent. We will use the natural logarithm (ln().

ln(3(x+2))=ln(20)

2. Use the power rule for logarithms, which states that ln(ab)=b*ln(a) to bring the exponent down as a multiplier.

(x+2)*ln(3)=ln(20)

3. Divide both sides by ln(3) to isolate the term containing x

x+2=ln(20)/ln(3)

4. Subtract 2 from both sides to solve for x

x=ln(20)/ln(3)−2

5. Simplify the expression if a decimal approximation is required, or keep it in exact form.

x≈2.7268−2

x≈0.7268

Final Answer

x=ln(20)/ln(3)−2

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