What is simplify-ln(7)+2ln(8)-(-ln(2)+2ln(3)) ?

The solution to simplify-ln(7)+2ln(8)-(-ln(2)+2ln(3)) is ln(64/7)-ln(9/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-ln(7)+2ln(8)-(-ln(2)+2ln(3))

simplify

- ln (7) + 2 ln (8) - (- ln (2) + 2 ln (3))

ln (\frac{64}{7}) - ln (\frac{9}{2})

Decimal Notation

0.70889 \dots

Solution steps

- ln (7) + 2 ln (8) - (- ln (2) + 2 ln (3))

Apply log rule:

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

2 ln (8) = ln (8^{2})

= - ln (7) + ln (8^{2}) - (2 ln (3) - ln (2))

Apply log rule:

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

ln (8^{2}) - ln (7) = ln (\frac{8 ^{2}}{7})

= ln (\frac{8 ^{2}}{7}) - (2 ln (3) - ln (2))

8^{2} = 64

= ln (\frac{64}{7}) - (- ln (2) + 2 ln (3))

Apply log rule:

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

2 ln (3) = ln (3^{2})

= ln (\frac{64}{7}) - (ln (3^{2}) - ln (2))

Apply log rule:

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

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

= ln (\frac{64}{7}) - (ln (\frac{3 ^{2}}{2}))

3^{2} = 9

= ln (\frac{64}{7}) - (ln (\frac{9}{2}))

Remove parentheses:

(a) = a

= ln (\frac{64}{7}) - ln (\frac{9}{2})

ln (x^{2} - 9) - ln (x + 3) + 2 ln (x)

ln (\frac{288}{353})

- ln (5.4 - 3) + 2 ln (5.4 - 2)

2 ln (x + 1) - ln (x - 2)

3 lo g_{7} (x) - 4 lo g_{7} (y)

What is simplify-ln(7)+2ln(8)-(-ln(2)+2ln(3)) ?
The solution to simplify-ln(7)+2ln(8)-(-ln(2)+2ln(3)) is ln(64/7)-ln(9/2)