What is the answer to log_{x+3}(3x^2+1)=2 ?

The answer to log_{x+3}(3x^2+1)=2 is x=-1,x=4

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log_{x+3}(3x^2+1)=2

lo g_{x + 3} (3 x^{2} + 1) = 2

x = - 1, x = 4

Solution steps

lo g_{x + 3} (3 x^{2} + 1) = 2

Apply log rules

\frac{ln ( 3 x ^{2} + 1 )}{ln ( x + 3 )} = 2

Multiply both sides by

ln (x + 3)

\frac{ln ( 3 x ^{2} + 1 )}{ln ( x + 3 )} ln (x + 3) = 2 ln (x + 3)

Simplify

ln (3 x^{2} + 1) = 2 ln (x + 3)

Apply log rules

3 x^{2} + 1 = (x + 3)^{2}

Solve

3 x^{2} + 1 = (x + 3)^{2} : x = - 1, x = 4

x = - 1, x = 4

Verify Solutions:

x = - 1

True

, x = 4

True

The solutions are

x = - 1, x = 4

lo g_{2} (2 + 5 x) = 3

lo g_{3} (x - 4) + lo g_{3} (x + 14) = 5

lo g_{2} (x) = 16

lo g_{4} (- 2 x + 8) = 3

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

What is the answer to log_{x+3}(3x^2+1)=2 ?
The answer to log_{x+3}(3x^2+1)=2 is x=-1,x=4
Solve for x: log_{x+3}(3x^2+1)=2
The solution is x=-1,x=4