What is the answer to log_{2x}(x^2+9x-6)=2 ?

The answer to log_{2x}(x^2+9x-6)=2 is x=1,x=2

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log_{2x}(x^2+9x-6)=2

lo g_{2 x} (x^{2} + 9 x - 6) = 2

x = 1, x = 2

Solution steps

lo g_{2 x} (x^{2} + 9 x - 6) = 2

Apply log rules

\frac{ln ( x ^{2} + 9 x - 6 )}{ln ( 2 x )} = 2

Multiply both sides by

ln (2 x)

\frac{ln ( x ^{2} + 9 x - 6 )}{ln ( 2 x )} ln (2 x) = 2 ln (2 x)

Simplify

ln (x^{2} + 9 x - 6) = 2 ln (2 x)

Apply log rules

x^{2} + 9 x - 6 = 4 x^{2}

Solve

x^{2} + 9 x - 6 = 4 x^{2} : x = 1, x = 2

x = 1, x = 2

Verify Solutions:

x = 1

True

, x = 2

True

The solutions are

x = 1, x = 2

lo g_{0.2} (2 x - 3) = - 1

ln (x) = \frac{x}{2}

0.1 x = ln (1 + 0.15 x)

lo g_{5} (\frac{2 x}{x - 1}) = 1

lo g_{3} (\frac{x}{5}) = 4

What is the answer to log_{2x}(x^2+9x-6)=2 ?
The answer to log_{2x}(x^2+9x-6)=2 is x=1,x=2
Solve for x: log_{2x}(x^2+9x-6)=2
The solution is x=1,x=2