What is 2log_{7}(x)+1/5 log_{7}(y)-2log_{7}(x+2) ?

The solution to 2log_{7}(x)+1/5 log_{7}(y)-2log_{7}(x+2) is log_{7}((x^2y^{1/5})/((x+2)^2))

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simplify 2log_{7}(x)+1/5 log_{7}(y)-2log_{7}(x+2)

simplify

2 lo g_{7} (x) + \frac{1}{5} lo g_{7} (y) - 2 lo g_{7} (x + 2)

lo g_{7} (\frac{x ^{2} y ^{\frac{1}{5}}}{( x + 2 ) ^{2}})

Solution steps

2 lo g_{7} (x) + \frac{1}{5} lo g_{7} (y) - 2 lo g_{7} (x + 2)

Apply log rule:

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

2 lo g_{7} (x) = lo g_{7} (x^{2})

= lo g_{7} (x^{2}) + \frac{1}{5} lo g_{7} (y) - 2 lo g_{7} (x + 2)

Apply log rule:

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

\frac{1}{5} lo g_{7} (y) = lo g_{7} (y^{\frac{1}{5}})

= lo g_{7} (x^{2}) + lo g_{7} (y^{\frac{1}{5}}) - 2 lo g_{7} (x + 2)

Apply log rule:

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

lo g_{7} (x^{2}) + lo g_{7} (y^{\frac{1}{5}}) = lo g_{7} (x^{2} y^{\frac{1}{5}})

= lo g_{7} (x^{2} y^{\frac{1}{5}}) - 2 lo g_{7} (x + 2)

Apply log rule:

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

2 lo g_{7} (x + 2) = lo g_{7} ((x + 2)^{2})

= lo g_{7} (x^{2} y^{\frac{1}{5}}) - lo g_{7} ((x + 2)^{2})

Apply log rule:

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

lo g_{7} (x^{2} y^{\frac{1}{5}}) - lo g_{7} ((x + 2)^{2}) = lo g_{7} (\frac{x ^{2} y ^{\frac{1}{5}}}{( x + 2 ) ^{2}})

= lo g_{7} (\frac{x ^{2} y ^{\frac{1}{5}}}{( x + 2 ) ^{2}})

lo g_{a} (2 x) + 2 (lo g_{a} (x) - lo g_{a} (y))

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

- lo g_{10} (3.3 \cdot 1 0^{- 11})

ln (5 x) + ln (2 y^{3}) - ln (x^{2} y)

What is 2log_{7}(x)+1/5 log_{7}(y)-2log_{7}(x+2) ?
The solution to 2log_{7}(x)+1/5 log_{7}(y)-2log_{7}(x+2) is log_{7}((x^2y^{1/5})/((x+2)^2))