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Popular >

simplify 1ln(x)-5/2 ln(y)

Solution

simplify

1 ln (x) - \frac{5}{2} ln (y)

Solution

ln (\frac{x}{y ^{\frac{5}{2}}})

Solution steps

1 \cdot ln (x) - \frac{5}{2} ln (y)

Apply log rule:

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

1 \cdot ln (x) = ln (x^{1})

= ln (x^{1}) - \frac{5}{2} ln (y)

Apply log rule:

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

\frac{5}{2} ln (y) = ln (y^{\frac{5}{2}})

= ln (x^{1}) - ln (y^{\frac{5}{2}})

Apply log rule:

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

ln (x^{1}) - ln (y^{\frac{5}{2}}) = ln (\frac{x ^{1}}{y ^{\frac{5}{2}}})

= ln (\frac{x ^{1}}{y ^{\frac{5}{2}}})

Apply rule

a^{1} = a

x^{1} = x

= ln (\frac{x}{y ^{\frac{5}{2}}})

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Frequently Asked Questions (FAQ)

What is 1ln(x)-5/2 ln(y) ?
The solution to 1ln(x)-5/2 ln(y) is ln(x/(y^{5/2)})