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Popular >

simplify 1/4 ln(16)+1/3 ln(125)

Solution

simplify

\frac{1}{4} ln (16) + \frac{1}{3} ln (125)

Solution

ln (10)

+1

Decimal Notation

2.30258 \dots

Solution steps

\frac{1}{4} ln (16) + \frac{1}{3} ln (125)

Apply log rule:

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

\frac{1}{4} ln (16) = ln (1 6^{\frac{1}{4}})

= ln (1 6^{\frac{1}{4}}) + \frac{1}{3} ln (125)

Apply log rule:

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

\frac{1}{3} ln (125) = ln (12 5^{\frac{1}{3}})

= ln (1 6^{\frac{1}{4}}) + ln (12 5^{\frac{1}{3}})

Apply log rule:

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

ln (1 6^{\frac{1}{4}}) + ln (12 5^{\frac{1}{3}}) = ln (1 6^{\frac{1}{4}} \cdot 12 5^{\frac{1}{3}})

= ln (1 6^{\frac{1}{4}} \cdot 12 5^{\frac{1}{3}})

1 6^{\frac{1}{4}} \cdot 12 5^{\frac{1}{3}} = 10

= ln (10)

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Frequently Asked Questions (FAQ)

What is 1/4 ln(16)+1/3 ln(125) ?
The solution to 1/4 ln(16)+1/3 ln(125) is ln(10)