What is the answer to log_{x-1}(x^3-2x^2+x-4)=3 ?

The answer to log_{x-1}(x^3-2x^2+x-4)=3 is x=3

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log_{x-1}(x^3-2x^2+x-4)=3

lo g_{x - 1} (x^{3} - 2 x^{2} + x - 4) = 3

x = 3

Solution steps

lo g_{x - 1} (x^{3} - 2 x^{2} + x - 4) = 3

Apply log rules

\frac{ln ( x ^{3} - 2 x ^{2} + x - 4 )}{ln ( x - 1 )} = 3

Multiply both sides by

ln (x - 1)

\frac{ln ( x ^{3} - 2 x ^{2} + x - 4 )}{ln ( x - 1 )} ln (x - 1) = 3 ln (x - 1)

Simplify

ln (x^{3} - 2 x^{2} + x - 4) = 3 ln (x - 1)

Apply log rules

x^{3} - 2 x^{2} + x - 4 = (x - 1)^{3}

Solve

x^{3} - 2 x^{2} + x - 4 = (x - 1)^{3} : x = 3, x = - 1

x = 3, x = - 1

Verify Solutions:

x = 3

True

, x = - 1

False

The solution is

x = 3

lo g_{3} (T) = \frac{1}{2}

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

7.1 = - lo g_{10} (x)

ln (x) = m x

lo g_{2} (5 x) = 2

What is the answer to log_{x-1}(x^3-2x^2+x-4)=3 ?
The answer to log_{x-1}(x^3-2x^2+x-4)=3 is x=3
Solve for x: log_{x-1}(x^3-2x^2+x-4)=3
The solution is x=3