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