What is simplify-2log_{10}(x+1)+log_{10}(x)+log_{10}(x^2-1) ?

The solution to simplify-2log_{10}(x+1)+log_{10}(x)+log_{10}(x^2-1) is log_{10}((x(x-1))/(x+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-2log_{10}(x+1)+log_{10}(x)+log_{10}(x^2-1)

simplify

- 2 lo g_{10} (x + 1) + lo g_{10} (x) + lo g_{10} (x^{2} - 1)

lo g_{10} (\frac{x ( x - 1 )}{x + 1})

Solution steps

- 2 lo g_{10} (x + 1) + lo g_{10} (x) + lo g_{10} (x^{2} - 1)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

- 2 lo g_{10} (x + 1) = - lo g_{10} ((x + 1)^{2})

= - lo g_{10} ((x + 1)^{2}) + lo g_{10} (x) + lo g_{10} (x^{2} - 1)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (x) - lo g_{10} ((x + 1)^{2}) = lo g_{10} (\frac{x}{( x + 1 ) ^{2}})

= lo g_{10} (\frac{x}{( x + 1 ) ^{2}}) + lo g_{10} (x^{2} - 1)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (\frac{x}{( x + 1 ) ^{2}}) + lo g_{10} (x^{2} - 1) = lo g_{10} (\frac{x}{( x + 1 ) ^{2}} (x^{2} - 1))

= lo g_{10} (\frac{x}{( x + 1 ) ^{2}} (x^{2} - 1))

Simplify

\frac{x}{( x + 1 ) ^{2}} (x^{2} - 1) : \frac{x ( x - 1 )}{x + 1}

= lo g_{10} (\frac{x ( x - 1 )}{x + 1})

lo g_{8} (\frac{9 x ^{3}}{4 y ^{2}})

lo g_{3} (\frac{x}{27})

lo g_{10} (3 b a)

ln (\frac{e ^{4}}{3})

What is simplify-2log_{10}(x+1)+log_{10}(x)+log_{10}(x^2-1) ?
The solution to simplify-2log_{10}(x+1)+log_{10}(x)+log_{10}(x^2-1) is log_{10}((x(x-1))/(x+1))