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Question

Solve ln 2 + ln x = 5
. Round to the nearest thousandth, if necessary.

Answer 1

To solve the equation ln 2 + ln x = 5, we can use the property of logarithms that states:

ln A + ln B = ln(AB)

Applying this property to the equation, we can rewrite it as:

ln (2x) = 5

Next, we need to eliminate the natural logarithm by exponentiating both sides of the equation. Exponentiating with base e (Euler's number) will cancel out the natural logarithm:

e^(ln(2x)) = e^5

Simplifying, we have:

2x = e^5

To solve for x, we substitute the value of e (approximately 2.71828) into the equation:

2x ≈ 2.71828^5

Using a calculator, we find:

2x ≈ 148.41316

To isolate x, we divide both sides of the equation by 2:

x ≈ 148.41316 / 2

Simplifying, we get:

x ≈ 74.20658

Therefore, the solution to ln 2 + ln x = 5, rounded to the nearest thousandth, is x ≈ 74.207.