Find all real solutions to the equation

siliciooy0j

siliciooy0j

Answered question

2022-04-02

Find all real solutions to the equation 31+2log3(yx)=48
With this problem I have difficulty getting rid of the exponent.
2log5(2yx12)=log5(yx)+log5(y+x)

Answer & Explanation

ineditablesdmx0

ineditablesdmx0

Beginner2022-04-03Added 9 answers

Hint: For the first equation, use 3a+b=3a3b, then the definition of log3 is that 3log3x= what?
For the second, raise 5 to the power of each side.
sa3b4or9i9

sa3b4or9i9

Beginner2022-04-04Added 14 answers

31+2log3(yx)=332log3(yx)=3(3log3(yx))2=3(yx)2 using alogax=x
3(yx)2=48(yx)2=16,y=x±4
From the 2nd equation, (2yx12)2=(yx)(y+x) using logx(ab)=logxa+logxb where x>0,1
If y=x+4,x=y4,2y(y4)122={y+y4}4
or (y8)2=4(2y4),y224y+80=0,y=20 or 4 using the solution of quadratic equation.
If y=20,x=204=16;y=4,x=44=0
Similarly, for y=x4

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