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Popular >

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

Solution

simplify

- 5 ln (2) - ln (3)

Solution

- ln (96)

+1

Decimal Notation

- 4.56434 \dots

Solution steps

- 5 ln (2) - ln (3)

Apply log rule:

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

5 ln (2) = ln (2^{5})

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

Rewrite

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

as

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

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

Apply log rule:

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

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

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

2^{5} \cdot 3 = 96

= - ln (96)

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Frequently Asked Questions (FAQ)

What is simplify-5ln(2)-ln(3) ?
The solution to simplify-5ln(2)-ln(3) is -ln(96)