Solve for t e^(3t)=900

Problem

e(3*t)=900

Solution

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

ln(e(3*t))=ln(900)

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

3*t=ln(900)

3. Isolate the variable t by dividing both sides of the equation by 3

t=ln(900)/3

4. Rewrite the expression if a decimal approximation is needed, though the exact form is often preferred.

t≈2.2674

Final Answer

t=ln(900)/3

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