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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 first combine the two logarithms using the addition property of logarithms:

ln 2 + ln x = ln(2x)

Thus, the equation can be simplified to:

ln(2x) = 5

Next, we can rewrite the equation in exponential form to solve for x. In exponential form, the natural logarithm equation becomes:

e^5 = 2x

To solve for x, divide both sides of the equation by 2:

x = e^5 / 2

Using a calculator, we can evaluate e^5 to be approximately 148.413.

x = 148.413 / 2

x ≈ 74.207

Rounded to the nearest thousandth, x ≈ 74.207.