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Popular >

simplify 4ln(tx)-2ln(x/(t^3))

Solution

simplify

4 ln (t x) - 2 ln (\frac{x}{t ^{3}})

Solution

ln (t^{10} x^{2})

Solution steps

4 ln (t x) - 2 ln (\frac{x}{t ^{3}})

Apply log rule:

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

4 ln (t x) = ln ((t x)^{4})

= ln ((t x)^{4}) - 2 ln (\frac{x}{t ^{3}})

Apply log rule:

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

2 ln (\frac{x}{t ^{3}}) = ln ((\frac{x}{t ^{3}})^{2})

= ln ((t x)^{4}) - ln ((\frac{x}{t ^{3}})^{2})

Apply log rule:

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

ln ((t x)^{4}) - ln ((\frac{x}{t ^{3}})^{2}) = ln (\frac{( t x ) ^{4}}{( \frac{x}{t ^{3}} ) ^{2}})

= ln (\frac{( t x ) ^{4}}{( \frac{x}{t ^{3}} ) ^{2}})

Simplify

\frac{( t x ) ^{4}}{( \frac{x}{t ^{3}} ) ^{2}} : t^{10} x^{2}

= ln (t^{10} x^{2})

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Frequently Asked Questions (FAQ)

What is 4ln(tx)-2ln(x/(t^3)) ?
The solution to 4ln(tx)-2ln(x/(t^3)) is ln(t^{10}x^2)