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Popular >

simplify 2/3 ln(a)+5ln(2)

Solution

simplify

\frac{2}{3} ln (a) + 5 ln (2)

Solution

ln (32 a^{\frac{2}{3}})

Solution steps

\frac{2}{3} ln (a) + 5 ln (2)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2^{5} = 32

= ln (32 a^{\frac{2}{3}})

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Frequently Asked Questions (FAQ)

What is 2/3 ln(a)+5ln(2) ?
The solution to 2/3 ln(a)+5ln(2) is ln(32a^{2/3})