What is 1/2 ln(2*9.5+1)+2ln(9.5-1) ?

The solution to 1/2 ln(2*9.5+1)+2ln(9.5-1) is ln(323.11182…)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/2 ln(2*9.5+1)+2ln(9.5-1)

simplify

\frac{1}{2} ln (2 \cdot 9.5 + 1) + 2 ln (9.5 - 1)

ln (323.11182 \dots)

Decimal Notation

5.77799 \dots

Solution steps

\frac{1}{2} ln (2 \cdot 9.5 + 1) + 2 ln (9.5 - 1)

Apply log rule:

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

\frac{1}{2} ln (2 \cdot 9.5 + 1) = ln ((2 \cdot 9.5 + 1)^{\frac{1}{2}})

= ln ((2 \cdot 9.5 + 1)^{\frac{1}{2}}) + 2 ln (9.5 - 1)

Apply log rule:

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

2 ln (9.5 - 1) = ln ((9.5 - 1)^{2})

= ln ((2 \cdot 9.5 + 1)^{\frac{1}{2}}) + ln ((9.5 - 1)^{2})

Apply log rule:

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

ln ((2 \cdot 9.5 + 1)^{\frac{1}{2}}) + ln ((9.5 - 1)^{2}) = ln ((9.5 - 1)^{2} (2 \cdot 9.5 + 1)^{\frac{1}{2}})

= ln ((9.5 - 1)^{2} (2 \cdot 9.5 + 1)^{\frac{1}{2}})

(2 \cdot 9.5 + 1)^{\frac{1}{2}} (9.5 - 1)^{2} = 323.11182 \dots

= ln (323.11182 \dots)

\frac{1}{0.0105} ln (\frac{8000}{5000})

ln (\frac{129}{1.22})

lo g_{7} (a^{2} b^{3} c)

38 ln (\frac{38}{21.21})

- 2 ln (5 x)

What is 1/2 ln(2*9.5+1)+2ln(9.5-1) ?
The solution to 1/2 ln(2*9.5+1)+2ln(9.5-1) is ln(323.11182…)