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Mnenie [13.5K]
3 years ago
10

Solve: 3 ln x = ln 216

Mathematics
2 answers:
BaLLatris [955]3 years ago
3 0

3\ln x=\ln 216\\ \ln x^3 =\ln 216\\ x^3=216\\ x=6

ella [17]3 years ago
3 0

To solve this problem, first we must understand that the coefficient of a log can also be expressed as the exponent of the argument. If we know this property, we can rewrite the equation as follows:


ln x^3 = ln 216


Next, we must use the inverse operation of ln to get rid of the logs on both sides. Because ln is really just a log with base e, if we make both sides of the equations the exponents of a base e, this will cancel the lns, and leave us with a simple equation.


e^ln(x^3) = e^ln216


This leaves us with:


x^3 = 216


If we take the cube root of each side to cancel out the degree 3 exponent on the variable x, we get that the answer is: x = 6 (Note: -6 is not an acceptable answer because (-6)^3 is actually -216).


Hope this helps!

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