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Solve The Exponential Equation. Exp E^(X-6)=25

User Cricket
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To solve the exponential equation e^(x - 6) = 25, you need to take the natural logarithm of both sides of the equation. This is possible because the logarithm and the exponential functions are inverse operations. The exponent of e on the left side of the equation comes down as a coefficient when taking the natural logarithm.

1. Start with the given equation: e^(x - 6) = 25.

2. Take the natural logarithm on both sides of the equation: ln(e^(x - 6)) = ln(25)

This simplifies because ln and e are inverse functions, so ln(e^(x - 6)) simplifies to x - 6.

3. So now the equation is x - 6 = ln(25).

4. The next step is to isolate x, which is done by adding 6 to both sides of the equation: x - 6 + 6 = ln(25) + 6. This gives you the equation x = ln(25) + 6.

5. Solve this equation for x: x = ln(25) + 6.

When you calculate the natural logarithm of 25 and add 6, the result is roughly 9.218875824868201.

Therefore, the solution to the equation e^(x-6) = 25 is x = 9.218875824868201.

User Smj
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