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Which equation is equivalent to
log3(2x4 + 8x3) – 3log3x = 2log3x?

log3(–x3 + 8x2) = log3x2

–2log3(2x4 + 8x3 – x) = log3x2

log3(2x + 8) = log3x2

(the 3 after the log is the base)

Respuesta :

CastleRook
This is the concept of algebra, to get the alternative form of the log expression below we simplified it as follows;

log3(2x^4+8x^3)-3log3x=2log3x
simplifying the above we get:
log3(2x^4+8x^3)=2log3x+3log3x
log3(2x^4+8x^3)=5log2x

Hence he answer should be:
log3 (x³)*(log3(2x+8))=5log3 x
3log3 x+log3(2x+8)=5log3 x
log3(2x+8)=5log3 x-3log3 x
log3 (2x+8)=2log3 x
log3 (2x+8)=log3 x²
the answer is log3 (2x+8)=log3 x²

The equation [tex]\rm log3(2x^4 + 8x^3) -3log3x = 2log3x[/tex] is equivalent to [tex]\rm log3(2x + 8) = log3x^2[/tex].

What is the log function?

The log function is defined as the inverse of the exponential function.

The given equation is;

[tex]\rm log3(2x^4 + 8x^3) -3log3x = 2log3x[/tex]

The equivalent equation is determined in the following steps given below.

[tex]\rm log3(2x^4 + 8x^3) -3log3x = 2log3x\\\\log3(2x^4+8x^3)=2log3x+3log3x\\\\ log3(2x^4+8x^3)=5log3x\\\\ log3 (x^3)\times (log3(2x+8))=5log3 x \\\\ 3log3 x+log3(2x+8)=5log3 x \\\\ log3(2x+8)=5log3 x-3log3 x \\\\log3 (2x+8)=2log3 x\\\\ log3 (2x+8)=log3 x^2[/tex]

Hence, the equation [tex]\rm log3(2x^4 + 8x^3) -3log3x = 2log3x[/tex] is equivalent to [tex]\rm log3(2x + 8) = log3x^2[/tex].

To know more about the log function click the link given below.

https://brainly.com/question/10781706

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