Solve for t e^(3t)=1000

Problem

e^(3*t)=1000

Solution

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

ln(e^(3*t))=ln(1000)

2. Simplify the left side using the property ln(e^x)=x

3*t=ln(1000)

3. Rewrite the constant on the right side by expressing 1000 as 10^3

3*t=ln(10^3)

4. Apply the power rule for logarithms, ln(a^b)=b*ln(a) to the right side.

3*t=3*ln(10)

5. Divide both sides by 3 to solve for t

t=ln(10)

Final Answer

t=ln(10)

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