What is ln(5)+6ln(x)-5ln(y) ?

The solution to ln(5)+6ln(x)-5ln(y) is ln((5x^6)/(y^5))

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simplify ln(5)+6ln(x)-5ln(y)

simplify

ln (5) + 6 ln (x) - 5 ln (y)

ln (\frac{5 x ^{6}}{y ^{5}})

Solution steps

ln (5) + 6 ln (x) - 5 ln (y)

Apply log rule:

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

6 ln (x) = ln (x^{6})

= ln (5) + ln (x^{6}) - 5 ln (y)

Apply log rule:

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

ln (5) + ln (x^{6}) = ln (5 x^{6})

= ln (5 x^{6}) - 5 ln (y)

Apply log rule:

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

5 ln (y) = ln (y^{5})

= ln (5 x^{6}) - ln (y^{5})

Apply log rule:

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

ln (5 x^{6}) - ln (y^{5}) = ln (\frac{5 x ^{6}}{y ^{5}})

= ln (\frac{5 x ^{6}}{y ^{5}})

ln (\frac{x}{a} \cdot e^{\frac{- x ^{2}}{( 2 a )}})

lo g_{10} (\frac{x ( x + 7 )}{( x + 3 ) ^{4}})

\frac{1}{2} lo g_{4} (16 x)

lo g_{0.5} (x + 1) - lo g_{0.5} (x - 3)

2 lo g_{6} (x - 7) + lo g_{6} (9) - 2

What is ln(5)+6ln(x)-5ln(y) ?
The solution to ln(5)+6ln(x)-5ln(y) is ln((5x^6)/(y^5))