What is the answer to log_{x+4}(3x^2-2x+16)=2 ?

The answer to log_{x+4}(3x^2-2x+16)=2 is x=5,x=0

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log_{x+4}(3x^2-2x+16)=2

lo g_{x + 4} (3 x^{2} - 2 x + 16) = 2

x = 5, x = 0

Solution steps

lo g_{x + 4} (3 x^{2} - 2 x + 16) = 2

Apply log rules

\frac{ln ( 3 x ^{2} - 2 x + 16 )}{ln ( x + 4 )} = 2

Multiply both sides by

ln (x + 4)

\frac{ln ( 3 x ^{2} - 2 x + 16 )}{ln ( x + 4 )} ln (x + 4) = 2 ln (x + 4)

Simplify

ln (3 x^{2} - 2 x + 16) = 2 ln (x + 4)

Apply log rules

3 x^{2} - 2 x + 16 = (x + 4)^{2}

Solve

3 x^{2} - 2 x + 16 = (x + 4)^{2} : x = 5, x = 0

x = 5, x = 0

Verify Solutions:

x = 5

True

, x = 0

True

The solutions are

x = 5, x = 0

lo g_{5} (x + 6) = 2

lo g_{10} (x) = 10.89

lo g_{10} (x + 4) = lo g_{10} (x) + lo g_{10} (4)

ln^{2} (x) + ln (x^{3}) + 2 = 0

lo g_{3} (x) = - \frac{1}{4}

What is the answer to log_{x+4}(3x^2-2x+16)=2 ?
The answer to log_{x+4}(3x^2-2x+16)=2 is x=5,x=0
Solve for x: log_{x+4}(3x^2-2x+16)=2
The solution is x=5,x=0