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Popular >

simplify 1/2 ln(9t^{10})-ln(3)

Solution

simplify

\frac{1}{2} ln (9 t^{10}) - ln (3)

Solution

ln (t^{5})

Solution steps

\frac{1}{2} ln (9 t^{10}) - ln (3)

Apply log rule:

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

\frac{1}{2} ln (9 t^{10}) = ln ((9 t^{10})^{\frac{1}{2}})

= ln ((9 t^{10})^{\frac{1}{2}}) - ln (3)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln ((9 t^{10})^{\frac{1}{2}}) - ln (3) = ln \frac{( 9 t ^{10} ) ^{\frac{1}{2}}}{3}

= ln \frac{( 9 t ^{10} ) ^{\frac{1}{2}}}{3}

Simplify

\frac{( 9 t ^{10} ) ^{\frac{1}{2}}}{3} : t^{5}

= ln (t^{5})

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Frequently Asked Questions (FAQ)

What is 1/2 ln(9t^{10})-ln(3) ?
The solution to 1/2 ln(9t^{10})-ln(3) is ln(t^5)