Solving Another Cool Exponential Equation

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PLAYLISTS 🎵 :

[winnewFirst]

Taking log to the base 3 is simpler, gives answer in the 2nd step.

[SweetSorrow]

Did you come up with this problem or you found this in some textbook?

[yousciencelab]

The two solutions are the same. Squaring log3 and taking under the square root with give exactly same result as the second method.

[justabunga]

Cross multiply this equation, which is 3^(x^2-4x+4)=2 or 3^((x-2)^2)=2. Taking log base 3 on both sides gives us (x-2)^2=log_3(2). Square root both sides, which is x-2=±√(log_3(2)). Solving for x gives us x=2±√(log_3(2)). Note that there's no further simplification if you combine the logarithms as the x value since √(log_3(2))=(log_3(2))^(1/2). Adding the 2 there won't make any difference to this value.

[vaggelissmyrniotis]

Complex solutions are x=2+-sqrt((ln2+2πni)/ln3).

[hubertczobodzinski]

What kind of software and hardware do you use?

[zygoloid]

Should really finish simplifying the answers: note that log_b x / log_b y = log_y x, so it's 2±√log_3(2).

[ViaanHossain]

Thanks for this kind of brainstorming questions.May Allah bless you ❤❤❤❤❤