Solve for t e^(0.04t)=1500

Problem

e^(0.04*t)=1500

Solution

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

ln(e^(0.04*t))=ln(1500)

2. Simplify the left side using the inverse property of logarithms, ln(e^x)=x

0.04*t=ln(1500)

3. Isolate the variable t by dividing both sides of the equation by 0.04

t=ln(1500)/0.04

4. Calculate the numerical value by performing the division.

t≈7.31322/0.04

t≈182.8305

Final Answer

t=ln(1500)/0.04≈182.8305

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