Solve log6-x(x^2-2x 1)/log3(x-1)-2

Question

Simplify the expression

\frac{lo g _{10} ( 6 ) \times lo g _{10} ( 3 ) - 2 lo g _{10} ( 3 ) - x ^{4} + 3 x ^{3} - 2 x ^{2}}{lo g _{10} ( 3 )}

Evaluate

lo g_{10} (6) - x \times \frac{x ^{2} - 2 x \times 1}{lo g _{10} ( 3 )} \times (x - 1) - 2

Multiply the terms

lo g_{10} (6) - x \times \frac{x ^{2} - 2 x}{lo g _{10} ( 3 )} \times (x - 1) - 2

Multiply the terms

More Steps

lo g_{10} (6) - \frac{x ( x ^{2} - 2 x ) ( x - 1 )}{lo g _{10} ( 3 )} - 2

Reduce fractions to a common denominator

\frac{lo g _{10} ( 6 ) \times lo g _{10} ( 3 )}{lo g _{10} ( 3 )} - \frac{x ( x ^{2} - 2 x ) ( x - 1 )}{lo g _{10} ( 3 )} - \frac{2 lo g _{10} ( 3 )}{lo g _{10} ( 3 )}

Write all numerators above the common denominator

\frac{lo g _{10} ( 6 ) \times lo g _{10} ( 3 ) - x ( x ^{2} - 2 x ) ( x - 1 ) - 2 lo g _{10} ( 3 )}{lo g _{10} ( 3 )}

Multiply the terms

More Steps

\frac{lo g _{10} ( 6 ) \times lo g _{10} ( 3 ) - ( x ^{4} - 3 x ^{3} + 2 x ^{2} ) - 2 lo g _{10} ( 3 )}{lo g _{10} ( 3 )}

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

\frac{lo g _{10} ( 6 ) \times lo g _{10} ( 3 ) - x ^{4} + 3 x ^{3} - 2 x ^{2} - 2 lo g _{10} ( 3 )}{lo g _{10} ( 3 )}

Solution

\frac{lo g _{10} ( 6 ) \times lo g _{10} ( 3 ) - 2 lo g _{10} ( 3 ) - x ^{4} + 3 x ^{3} - 2 x ^{2}}{lo g _{10} ( 3 )}

Show Solution