What is 2ln(x)-1/2 ln(x+5) ?

The solution to 2ln(x)-1/2 ln(x+5) is ln((x^2sqrt(x+5))/(x+5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2ln(x)-1/2 ln(x+5)

simplify

2 ln (x) - \frac{1}{2} ln (x + 5)

ln (\frac{x ^{2} x + 5}{x + 5})

Solution steps

2 ln (x) - \frac{1}{2} ln (x + 5)

Apply log rule:

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

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

= ln (x^{2}) - \frac{1}{2} ln (x + 5)

Apply log rule:

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

\frac{1}{2} ln (x + 5) = ln ((x + 5)^{\frac{1}{2}})

= ln (x^{2}) - ln ((x + 5)^{\frac{1}{2}})

Apply log rule:

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

ln (x^{2}) - ln ((x + 5)^{\frac{1}{2}}) = ln (\frac{x ^{2}}{( x + 5 ) ^{\frac{1}{2}}})

= ln (\frac{x ^{2}}{( x + 5 ) ^{\frac{1}{2}}})

Simplify

\frac{x ^{2}}{( x + 5 ) ^{\frac{1}{2}}} : \frac{x ^{2} x + 5}{x + 5}

= ln (\frac{x ^{2} x + 5}{x + 5})

4^{\frac{l n ( \frac{4}{3} )}{3 l n ( 2 )}}

ln (5 x) + ln (3 x)

- lo g_{10} (1.3 x 1 0^{- 4})

π \cdot ln (\frac{7}{3})

lo g_{10} (2 x^{2})

What is 2ln(x)-1/2 ln(x+5) ?
The solution to 2ln(x)-1/2 ln(x+5) is ln((x^2sqrt(x+5))/(x+5))