What is simplify-4ln(2)-3ln(3)-4ln(5) ?

The solution to simplify-4ln(2)-3ln(3)-4ln(5) is -ln(432)-4ln(5)

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simplify-4ln(2)-3ln(3)-4ln(5)

simplify

- 4 ln (2) - 3 ln (3) - 4 ln (5)

- ln (432) - 4 ln (5)

Decimal Notation

- 12.50617 \dots

Solution steps

- 4 ln (2) - 3 ln (3) - 4 ln (5)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Rewrite

- ln (2^{4}) - ln (3^{3})

- (ln (2^{4}) + ln (3^{3}))

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

Apply log rule:

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

ln (2^{4}) + ln (3^{3}) = ln (2^{4} \cdot 3^{3})

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

2^{4} \cdot 3^{3} = 432

= - ln (432) - 4 ln (5)

3 ln (+ \frac{1}{3} ln (y))

2 ln (\frac{201}{8})

- 1 - 5 \cdot ln (\frac{1.5}{4})

ln (\frac{1}{999})

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

What is simplify-4ln(2)-3ln(3)-4ln(5) ?
The solution to simplify-4ln(2)-3ln(3)-4ln(5) is -ln(432)-4ln(5)