What is the answer to log_{x-3}(x^2-3x-4)=2 ?

The answer to log_{x-3}(x^2-3x-4)=2 is x= 13/3

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log_{x-3}(x^2-3x-4)=2

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

x = \frac{13}{3}

Decimal Notation

x = 4.33333 \dots

Solution steps

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

Apply log rules

\frac{ln ( x ^{2} - 3 x - 4 )}{ln ( x - 3 )} = 2

Multiply both sides by

ln (x - 3)

\frac{ln ( x ^{2} - 3 x - 4 )}{ln ( x - 3 )} ln (x - 3) = 2 ln (x - 3)

Simplify

ln (x^{2} - 3 x - 4) = 2 ln (x - 3)

Apply log rules

x^{2} - 3 x - 4 = (x - 3)^{2}

Solve

x^{2} - 3 x - 4 = (x - 3)^{2} : x = \frac{13}{3}

x = \frac{13}{3}

Verify Solutions:

x = \frac{13}{3}

True

The solution is

x = \frac{13}{3}

ln (x) + ln (5 - 2 x) = 0

lo g_{6561} (N) = - \frac{3}{4}

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

x, ln (x) = a + b (ln (y))

\frac{1}{2} ln (4 + c) = 0

What is the answer to log_{x-3}(x^2-3x-4)=2 ?
The answer to log_{x-3}(x^2-3x-4)=2 is x= 13/3
Solve for x: log_{x-3}(x^2-3x-4)=2
The solution is x= 13/3