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Popular >

simplify ln(3)+4ln(2)-ln(6)

Solution

simplify

ln (3) + 4 ln (2) - ln (6)

Solution

3 ln (2)

+1

Decimal Notation

2.07944 \dots

Solution steps

ln (3) + 4 ln (2) - ln (6)

Apply log rule:

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

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

= ln (3) + ln (2^{4}) - ln (6)

Apply log rule:

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

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

= ln (2^{4} \cdot 3) - ln (6)

3 \cdot 2^{4} = 48

= ln (48) - ln (6)

Apply log rule:

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

ln (48) - ln (6) = ln (\frac{48}{6})

= ln (\frac{48}{6})

Divide the numbers:

\frac{48}{6} = 8

= ln (8)

Rewrite

8

in power-base form:

8 = 2^{3}

= ln (2^{3})

Apply log rule:

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

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

= 3 ln (2)

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Frequently Asked Questions (FAQ)

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