What is the answer to log_{2x}(3x^2+9x-20)=2 ?

The answer to log_{2x}(3x^2+9x-20)=2 is x=4,x=5

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log_{2x}(3x^2+9x-20)=2

lo g_{2 x} (3 x^{2} + 9 x - 20) = 2

x = 4, x = 5

Solution steps

lo g_{2 x} (3 x^{2} + 9 x - 20) = 2

Apply log rules

\frac{ln ( 3 x ^{2} + 9 x - 20 )}{ln ( 2 x )} = 2

Multiply both sides by

ln (2 x)

\frac{ln ( 3 x ^{2} + 9 x - 20 )}{ln ( 2 x )} ln (2 x) = 2 ln (2 x)

Simplify

ln (3 x^{2} + 9 x - 20) = 2 ln (2 x)

Apply log rules

3 x^{2} + 9 x - 20 = 4 x^{2}

Solve

3 x^{2} + 9 x - 20 = 4 x^{2} : x = 4, x = 5

x = 4, x = 5

Verify Solutions:

x = 4

True

, x = 5

True

The solutions are

x = 4, x = 5

4 = lo g_{x} (625)

7 x^{6} ln (x) + x^{6} = 0

lo g_{3} (6 - x) = 3

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

lo g_{5} (x - 5) = 3

What is the answer to log_{2x}(3x^2+9x-20)=2 ?
The answer to log_{2x}(3x^2+9x-20)=2 is x=4,x=5
Solve for x: log_{2x}(3x^2+9x-20)=2
The solution is x=4,x=5