What is the answer to log_{2x}(3x^2+9x-18)=2 ?

The answer to log_{2x}(3x^2+9x-18)=2 is x=3,x=6

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log_{2x}(3x^2+9x-18)=2

lo g_{2 x} (3 x^{2} + 9 x - 18) = 2

x = 3, x = 6

Solution steps

lo g_{2 x} (3 x^{2} + 9 x - 18) = 2

Apply log rules

\frac{ln ( 3 x ^{2} + 9 x - 18 )}{ln ( 2 x )} = 2

Multiply both sides by

ln (2 x)

\frac{ln ( 3 x ^{2} + 9 x - 18 )}{ln ( 2 x )} ln (2 x) = 2 ln (2 x)

Simplify

ln (3 x^{2} + 9 x - 18) = 2 ln (2 x)

Apply log rules

3 x^{2} + 9 x - 18 = 4 x^{2}

Solve

3 x^{2} + 9 x - 18 = 4 x^{2} : x = 3, x = 6

x = 3, x = 6

Verify Solutions:

x = 3

True

, x = 6

True

The solutions are

x = 3, x = 6

lo g_{2} (a) = 4

lo g_{\frac{1}{2}} (x + 4) = 0

lo g_{10} (2^{x}) = lo g_{10} (4^{x + 2})

lo g_{x} (0.015625) = 3

a, lo g_{ab} (a) = 3

What is the answer to log_{2x}(3x^2+9x-18)=2 ?
The answer to log_{2x}(3x^2+9x-18)=2 is x=3,x=6
Solve for x: log_{2x}(3x^2+9x-18)=2
The solution is x=3,x=6