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Popular >

simplify 2ln(6.3)-2ln(2.1)

Solution

simplify

2 ln (6.3) - 2 ln (2.1)

Solution

2 ln (3)

+1

Decimal Notation

2.19722 \dots

Solution steps

2 ln (6.3) - 2 ln (2.1)

Apply log rule:

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

2 ln (6.3) = ln (6. 3^{2})

= ln (6. 3^{2}) - 2 ln (2.1)

Apply log rule:

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

2 ln (2.1) = ln (2. 1^{2})

= ln (6. 3^{2}) - ln (2. 1^{2})

Apply log rule:

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

ln (6. 3^{2}) - ln (2. 1^{2}) = ln (\frac{6. 3 ^{2}}{2. 1 ^{2}})

= ln (\frac{6. 3 ^{2}}{2. 1 ^{2}})

\frac{6. 3 ^{2}}{2. 1 ^{2}} = 9

= ln (9)

Rewrite

9

in power-base form:

9 = 3^{2}

= ln (3^{2})

Apply log rule:

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

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

= 2 ln (3)

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Frequently Asked Questions (FAQ)

What is 2ln(6.3)-2ln(2.1) ?
The solution to 2ln(6.3)-2ln(2.1) is 2ln(3)