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Popular >

simplify 1/2 ln(4t^4)-ln(b)

Solution

simplify

\frac{1}{2} ln (4 t^{4}) - ln (b)

Solution

ln (\frac{2 t ^{2}}{b})

Solution steps

\frac{1}{2} ln (4 t^{4}) - ln (b)

Apply log rule:

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

\frac{1}{2} ln (4 t^{4}) = ln ((4 t^{4})^{\frac{1}{2}})

= ln ((4 t^{4})^{\frac{1}{2}}) - ln (b)

Apply log rule:

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

ln ((4 t^{4})^{\frac{1}{2}}) - ln (b) = ln \frac{( 4 t ^{4} ) ^{\frac{1}{2}}}{b}

= ln \frac{( 4 t ^{4} ) ^{\frac{1}{2}}}{b}

(4 t^{4})^{\frac{1}{2}} = 2 t^{2}

= ln (\frac{2 t ^{2}}{b})

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Frequently Asked Questions (FAQ)

What is 1/2 ln(4t^4)-ln(b) ?
The solution to 1/2 ln(4t^4)-ln(b) is ln((2t^2)/b)