What is ln(5)+1+ln(y)-7ln(x) ?

The solution to ln(5)+1+ln(y)-7ln(x) is ln((5y)/(x^7))+1

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simplify ln(5)+1+ln(y)-7ln(x)

simplify

ln (5) + 1 + ln (y) - 7 ln (x)

ln (\frac{5 y}{x ^{7}}) + 1

Solution steps

ln (5) + 1 + ln (y) - 7 ln (x)

Apply log rule:

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

ln (5) + ln (y) = ln (5 y)

= ln (5 y) + 1 - 7 ln (x)

Apply log rule:

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

7 ln (x) = ln (x^{7})

= ln (5 y) + 1 - ln (x^{7})

Apply log rule:

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

ln (5 y) - ln (x^{7}) = ln (\frac{5 y}{x ^{7}})

= ln (\frac{5 y}{x ^{7}}) + 1

ln (\frac{e ^{8}}{19})

lo g_{10} (3) + 2 lo g_{10} (x) - 3 lo g_{10} (y)

lo g_{2} (\frac{1}{\frac{1}{6}})

\frac{1}{2} lo g_{10} (x) - lo g_{10} (y)

ln (2) + 0.9 \cdot ln (2.25)

What is ln(5)+1+ln(y)-7ln(x) ?
The solution to ln(5)+1+ln(y)-7ln(x) is ln((5y)/(x^7))+1