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Popular >

simplify 1/3 ln(2)+1/3 ln(10)

Solution

simplify

\frac{1}{3} ln (2) + \frac{1}{3} ln (10)

Solution

\frac{1}{3} ln (20)

+1

Decimal Notation

0.99857 \dots

Solution steps

\frac{1}{3} ln (2) + \frac{1}{3} ln (10)

Apply log rule:

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

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

= ln (2^{\frac{1}{3}}) + \frac{1}{3} ln (10)

Apply log rule:

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

\frac{1}{3} ln (10) = ln (1 0^{\frac{1}{3}})

= ln (2^{\frac{1}{3}}) + ln (1 0^{\frac{1}{3}})

Apply log rule:

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

ln (2^{\frac{1}{3}}) + ln (1 0^{\frac{1}{3}}) = ln (2^{\frac{1}{3}} \cdot 1 0^{\frac{1}{3}})

= ln (2^{\frac{1}{3}} \cdot 1 0^{\frac{1}{3}})

Rewrite as

= ln (2 0^{\frac{1}{3}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{3} ln (20)

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Frequently Asked Questions (FAQ)

What is 1/3 ln(2)+1/3 ln(10) ?
The solution to 1/3 ln(2)+1/3 ln(10) is 1/3 ln(20)