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Popular >

simplify 2ln(7)-2ln(3.5)

Solution

simplify

2 ln (7) - 2 ln (3.5)

Solution

2 ln (2)

+1

Decimal Notation

1.38629 \dots

Solution steps

2 ln (7) - 2 ln (3.5)

Apply log rule:

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

2 ln (7) = ln (7^{2})

= ln (7^{2}) - 2 ln (3.5)

Apply log rule:

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

2 ln (3.5) = ln (3. 5^{2})

= ln (7^{2}) - ln (3. 5^{2})

Apply log rule:

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

ln (7^{2}) - ln (3. 5^{2}) = ln (\frac{7 ^{2}}{3. 5 ^{2}})

= ln (\frac{7 ^{2}}{3. 5 ^{2}})

\frac{7 ^{2}}{3. 5 ^{2}} = 4

= ln (4)

Rewrite

4

in power-base form:

4 = 2^{2}

= ln (2^{2})

Apply log rule:

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

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

= 2 ln (2)

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Frequently Asked Questions (FAQ)

What is 2ln(7)-2ln(3.5) ?
The solution to 2ln(7)-2ln(3.5) is 2ln(2)