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Popular >

simplify 3ln(4)+4ln(3)-4ln(3)

Solution

simplify

3 ln (4) + 4 ln (3) - 4 ln (3)

Solution

6 ln (2)

+1

Decimal

4.15888 \dots

Solution steps

3 ln (4) + 4 ln (3) - 4 ln (3)

Apply log rule:

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

3 ln (4) = ln (4^{3})

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

Apply log rule:

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

4 ln (3) = ln (3^{4})

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

Apply log rule:

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

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

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

4^{3} \cdot 3^{4} = 5184

= ln (5184) - 4 ln (3)

Apply log rule:

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

4 ln (3) = ln (3^{4})

= ln (5184) - ln (3^{4})

Apply log rule:

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

ln (5184) - ln (3^{4}) = ln (\frac{5184}{3 ^{4}})

= ln (\frac{5184}{3 ^{4}})

\frac{5184}{3 ^{4}} = 64

= ln (64)

Rewrite

64

in power-base form:

64 = 2^{6}

= ln (2^{6})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (2^{6}) = 6 ln (2)

= 6 ln (2)

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Frequently Asked Questions (FAQ)

What is 3ln(4)+4ln(3)-4ln(3) ?
The solution to 3ln(4)+4ln(3)-4ln(3) is 6ln(2)