Ln( x + 3 ) = 2Ln4, Good in Algebra? Should be able to solve FAST with NO Calculator!

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Lesson on how to solve a natural logarithmic equation.
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20 янв 2024

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Комментарии : 23

@statseasy4780 6 месяцев назад

Nice. You could also do this: on the right, use the entire right side as an exponent on e without using the 2 as an exponent on 4 (yet). So we have e^2ln4. That can also be written (e^2)^ln4, but it's more useful as (e^ln4)^2, which is equivalent. This is 4^2, which is 16. X + 3 = 16; x = 16 - 3 = 13.

@laurendoe168 6 месяцев назад

I just changed 2ln4 to ln4^2, then erased the ln, leaving x+3 = 4^2, aka x+3 = 16

@laurendoe168 6 месяцев назад

If you can "ln both sides", you can "un-ln both sides"

@quigonkenny 6 месяцев назад

Yep. Only reason ln is there is just to tell you that the 2 is an exponent of the 4. Only reason you'd need to do any actual logarithmic calculation is if the bases were different or one side didn't contain a ln.

@moonmissionpassagetototali1952 6 месяцев назад

This solution is also correct: e^ln(x+3) = x+3 = e^2ln4. x = e^2ln4 - 3. Use calculator to find e^2ln4 = 16. Therefore x = 13.

@terry_willis 6 месяцев назад

If the problem had been stated with "log" (regular logs) instead of "ln" (natural logs) would the solution process (and answer) been the same?

@davidellis1079 6 месяцев назад

Yes. In fact the logs could be in any base, as long as they both have the same base.

@quigonkenny 6 месяцев назад

Yes. ln(x) just means logₑ(x). Only difference is the base of the log, and in the case of this problem that doesn't even need to come into play. Since the equation is simply a comparison of two logarithmic values, the bases don't matter as long as they're the same base, since what are being compared are their arguments. The "ln" or "log" might as well not be there except to define how the "2" on the right side of the equation is handled, and that's the same for all bases.

@terry_willis 6 месяцев назад

@@quigonkenny Thank you.