What is 1/2 (ln(3^2)-ln(5^4)-ln(2^2)) ?

The solution to 1/2 (ln(3^2)-ln(5^4)-ln(2^2)) is 1/2 ln(9/2500)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/2 (ln(3^2)-ln(5^4)-ln(2^2))

simplify

\frac{1}{2} (ln (3^{2}) - ln (5^{4}) - ln (2^{2}))

\frac{1}{2} ln (\frac{9}{2500})

Decimal Notation

- 2.81341 \dots

Solution steps

\frac{1}{2} (ln (3^{2}) - ln (5^{4}) - ln (2^{2}))

Apply log rule:

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

ln (3^{2}) - ln (5^{4}) = ln (\frac{3 ^{2}}{5 ^{4}})

= \frac{1}{2} (ln (\frac{3 ^{2}}{5 ^{4}}) - ln (2^{2}))

\frac{3 ^{2}}{5 ^{4}} = \frac{9}{625}

= \frac{1}{2} (ln (\frac{9}{625}) - ln (2^{2}))

Apply log rule:

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

ln (\frac{9}{625}) - ln (2^{2}) = ln (\frac{\frac{9}{625}}{2 ^{2}})

= \frac{1}{2} ln (\frac{\frac{9}{625}}{2 ^{2}})

\frac{\frac{9}{625}}{2 ^{2}} = \frac{9}{2500}

= \frac{1}{2} ln (\frac{9}{2500})

lo g_{10} (z^{45})

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

ln (e^{2} - e^{- 2}) - ln (e - e^{- 1})

ln ∣ x - 1 ∣ - ln ∣ x + 4 ∣

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

What is 1/2 (ln(3^2)-ln(5^4)-ln(2^2)) ?
The solution to 1/2 (ln(3^2)-ln(5^4)-ln(2^2)) is 1/2 ln(9/2500)