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Popular >

simplify 1/2 ln(a)+2ln(c)

Solution

simplify

\frac{1}{2} ln (a) + 2 ln (c)

Solution

ln (a^{\frac{1}{2}} c^{2})

Solution steps

\frac{1}{2} ln (a) + 2 ln (c)

Apply log rule:

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

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

= ln (a^{\frac{1}{2}}) + 2 ln (c)

Apply log rule:

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

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

= ln (a^{\frac{1}{2}}) + ln (c^{2})

Apply log rule:

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

ln (a^{\frac{1}{2}}) + ln (c^{2}) = ln (c^{2} a^{\frac{1}{2}})

= ln (a^{\frac{1}{2}} c^{2})

Popular Examples

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Frequently Asked Questions (FAQ)

What is 1/2 ln(a)+2ln(c) ?
The solution to 1/2 ln(a)+2ln(c) is ln(a^{1/2}c^2)