What is the answer to log_{x}(3x^2-13x+15)=2 ?

The answer to log_{x}(3x^2-13x+15)=2 is x=5,x= 3/2

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log_{x}(3x^2-13x+15)=2

lo g_{x} (3 x^{2} - 13 x + 15) = 2

x = 5, x = \frac{3}{2}

Decimal Notation

x = 5, x = 1.5

Solution steps

lo g_{x} (3 x^{2} - 13 x + 15) = 2

Apply log rules

\frac{ln ( 3 x ^{2} - 13 x + 15 )}{ln ( x )} = 2

Multiply both sides by

ln (x)

\frac{ln ( 3 x ^{2} - 13 x + 15 )}{ln ( x )} ln (x) = 2 ln (x)

Simplify

ln (3 x^{2} - 13 x + 15) = 2 ln (x)

Apply log rules

3 x^{2} - 13 x + 15 = x^{2}

Solve

3 x^{2} - 13 x + 15 = x^{2} : x = 5, x = \frac{3}{2}

x = 5, x = \frac{3}{2}

Verify Solutions:

x = 5

True

, x = \frac{3}{2}

True

The solutions are

x = 5, x = \frac{3}{2}

- 2 ln (5 x) = ln (9) - ln (5)

lo g_{x} (\frac{1}{64}) = 2

lo g_{10} (x) = - 4138

1 = ln (x - 2)

lo g_{7} (4 x + 30) = lo g_{7} (72)

What is the answer to log_{x}(3x^2-13x+15)=2 ?
The answer to log_{x}(3x^2-13x+15)=2 is x=5,x= 3/2
Solve for x: log_{x}(3x^2-13x+15)=2
The solution is x=5,x= 3/2