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Popular >

simplify 2ln(7)-3ln(2)+2ln(5)

Solution

simplify

2 ln (7) - 3 ln (2) + 2 ln (5)

Solution

ln (\frac{1225}{8})

+1

Decimal Notation

5.03125 \dots

Solution steps

2 ln (7) - 3 ln (2) + 2 ln (5)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{7 ^{2}}{2 ^{3}} = \frac{49}{8}

= ln (\frac{49}{8}) + 2 ln (5)

Apply log rule:

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

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

= ln (\frac{49}{8}) + ln (5^{2})

Apply log rule:

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

ln (\frac{49}{8}) + ln (5^{2}) = ln (5^{2} \cdot \frac{49}{8})

= ln (5^{2} \cdot \frac{49}{8})

\frac{49}{8} \cdot 5^{2} = \frac{1225}{8}

= ln (\frac{1225}{8})

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Frequently Asked Questions (FAQ)

What is 2ln(7)-3ln(2)+2ln(5) ?
The solution to 2ln(7)-3ln(2)+2ln(5) is ln(1225/8)