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Popular >

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

Solution

simplify

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

Solution

- ln (800)

+1

Decimal Notation

- 6.68461 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Rewrite

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

as

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

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

Apply log rule:

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

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

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

4^{4} \cdot 5^{2} = 6400

= 3 ln (2) - ln (6400)

Apply log rule:

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

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

= ln (2^{3}) - ln (6400)

Apply log rule:

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

ln (2^{3}) - ln (6400) = ln (\frac{2 ^{3}}{6400})

= ln (\frac{2 ^{3}}{6400})

\frac{2 ^{3}}{6400} = \frac{1}{800}

= ln (\frac{1}{800})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (800)

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Frequently Asked Questions (FAQ)

What is 3ln(2)-4ln(4)-2ln(5) ?
The solution to 3ln(2)-4ln(4)-2ln(5) is -ln(800)