What is the answer to log_{x}(2x^2-8x+15)=2 ?

The answer to log_{x}(2x^2-8x+15)=2 is x=5,x=3

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log_{x}(2x^2-8x+15)=2

lo g_{x} (2 x^{2} - 8 x + 15) = 2

x = 5, x = 3

Solution steps

lo g_{x} (2 x^{2} - 8 x + 15) = 2

Apply log rules

\frac{ln ( 2 x ^{2} - 8 x + 15 )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( 2 x ^{2} - 8 x + 15 )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (2 x^{2} - 8 x + 15) = 2 ln (x)

Apply log rules

2 x^{2} - 8 x + 15 = x^{2}

Solve

2 x^{2} - 8 x + 15 = x^{2} : x = 5, x = 3

x = 5, x = 3

Verify Solutions:

x = 5

True

, x = 3

True

The solutions are

x = 5, x = 3

0 = 1 - ln (x - 1)

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

20 lo g_{10} (x) = 45

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

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

What is the answer to log_{x}(2x^2-8x+15)=2 ?
The answer to log_{x}(2x^2-8x+15)=2 is x=5,x=3
Solve for x: log_{x}(2x^2-8x+15)=2
The solution is x=5,x=3