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Popular >

simplify 2ln(5)+4ln(3)

Solution

simplify

2 ln (5) + 4 ln (3)

Solution

2 ln (45)

+1

Decimal Notation

7.61332 \dots

Solution steps

2 ln (5) + 4 ln (3)

Apply log rule:

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

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

= ln (5^{2}) + 4 ln (3)

Apply log rule:

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

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

= ln (5^{2}) + ln (3^{4})

Apply log rule:

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

ln (5^{2}) + ln (3^{4}) = ln (3^{4} \cdot 5^{2})

= ln (3^{4} \cdot 5^{2})

5^{2} \cdot 3^{4} = 2025

= ln (2025)

Rewrite

2025

in power-base form:

2025 = 4 5^{2}

= ln (4 5^{2})

Apply log rule:

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

ln (4 5^{2}) = 2 ln (45)

= 2 ln (45)

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Frequently Asked Questions (FAQ)

What is 2ln(5)+4ln(3) ?
The solution to 2ln(5)+4ln(3) is 2ln(45)