What is the answer to log_{2x-1}(3x^2+6)=2 ?

The answer to log_{2x-1}(3x^2+6)=2 is x=5

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log_{2x-1}(3x^2+6)=2

lo g_{2 x - 1} (3 x^{2} + 6) = 2

x = 5

Solution steps

lo g_{2 x - 1} (3 x^{2} + 6) = 2

Apply log rules

\frac{ln ( 3 x ^{2} + 6 )}{ln ( 2 x - 1 )} = 2

Multiply both sides by

ln (2 x - 1)

\frac{ln ( 3 x ^{2} + 6 )}{ln ( 2 x - 1 )} ln (2 x - 1) = 2 ln (2 x - 1)

Simplify

ln (3 x^{2} + 6) = 2 ln (2 x - 1)

Apply log rules

3 x^{2} + 6 = (2 x - 1)^{2}

Solve

3 x^{2} + 6 = (2 x - 1)^{2} : x = 5, x = - 1

x = 5, x = - 1

Verify Solutions:

x = 5

True

, x = - 1

False

The solution is

x = 5

0 = ln (x - 1) + 2

0 = ln (x - 1) - 2

0.367 = 2 - lo g_{10} (x)

lo g_{a} (64) = - 2

x + lo g_{10} (x + 4) = 6

What is the answer to log_{2x-1}(3x^2+6)=2 ?
The answer to log_{2x-1}(3x^2+6)=2 is x=5
Solve for x: log_{2x-1}(3x^2+6)=2
The solution is x=5