What is 2ln(x-4)-ln(x+4)-ln(x^2-16)+ln(4)+ln(x) ?

The solution to 2ln(x-4)-ln(x+4)-ln(x^2-16)+ln(4)+ln(x) is ln((4x(x-4))/((x+4)^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2ln(x-4)-ln(x+4)-ln(x^2-16)+ln(4)+ln(x)

simplify

2 ln (x - 4) - ln (x + 4) - ln (x^{2} - 16) + ln (4) + ln (x)

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

Solution steps

2 ln (x - 4) - ln (x + 4) - ln (x^{2} - 16) + ln (4) + ln (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln ((x - 4)^{2}) - ln (x + 4) - ln (x^{2} - 16) + ln (4) + ln (x)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

= ln (\frac{( x - 4 ) ^{2}}{x + 4}) - ln (x^{2} - 16) + ln (4) + ln (x)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (\frac{( x - 4 ) ^{2}}{x + 4}) - ln (x^{2} - 16) = ln (\frac{\frac{( x - 4 ) ^{2}}{x + 4}}{x ^{2} - 16})

= ln (\frac{\frac{( x - 4 ) ^{2}}{x + 4}}{x ^{2} - 16}) + ln (4) + ln (x)

Simplify

\frac{\frac{( x - 4 ) ^{2}}{x + 4}}{x ^{2} - 16} : \frac{x - 4}{( x + 4 ) ^{2}}

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

ln (x) + ln (y) + \frac{x \frac{d y}{d x} + y}{y}

\frac{1}{2} ln (1 + (\frac{y}{x})^{2}) + ln (x)

- \frac{1}{2} ln (2 + x) - \frac{1}{2} ln (2 - x)

ln (θ e^{- n (x^{1} + x^{2} + x^{3})})

ln (\frac{225 - 0.9}{( 2.82108 - 0.9 )})

What is 2ln(x-4)-ln(x+4)-ln(x^2-16)+ln(4)+ln(x) ?
The solution to 2ln(x-4)-ln(x+4)-ln(x^2-16)+ln(4)+ln(x) is ln((4x(x-4))/((x+4)^2))