Solve for x 5^(2x)=20

Problem

5(2*x)=20

Solution

1. Apply the natural logarithm to both sides of the equation to isolate the exponent.

ln(5(2*x))=ln(20)

2. Use the power rule for logarithms, ln(ab)=b*ln(a) to move the exponent in front of the logarithm.

2*x*ln(5)=ln(20)

3. Isolate the variable x by dividing both sides by 2*ln(5)

x=ln(20)/(2*ln(5))

4. Simplify the expression using the property ln(20)=ln(4⋅5)=ln(4)+ln(5) if a different form is desired, or calculate the numerical value.

x=(ln(4)+ln(5))/(2*ln(5))

5. Further simplify by dividing the terms in the numerator.

x=ln(4)/(2*ln(5))+ln(5)/(2*ln(5))

x=(2*ln(2))/(2*ln(5))+1/2

x=ln(2)/ln(5)+1/2

Final Answer

x=ln(20)/(2*ln(5))

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