What is simplify-2/3 log_{10}(x)-2log_{10}(y) ?

The solution to simplify-2/3 log_{10}(x)-2log_{10}(y) is -log_{10}(x^{2/3}y^2)

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simplify-2/3 log_{10}(x)-2log_{10}(y)

simplify

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

- lo g_{10} (x^{\frac{2}{3}} y^{2})

Solution steps

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

Apply log rule:

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

\frac{2}{3} lo g_{10} (x) = lo g_{10} (x^{\frac{2}{3}})

= - lo g_{10} (x^{\frac{2}{3}}) - 2 lo g_{10} (y)

Apply log rule:

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

2 lo g_{10} (y) = lo g_{10} (y^{2})

= - lo g_{10} (x^{\frac{2}{3}}) - lo g_{10} (y^{2})

Rewrite

- lo g_{10} (x^{\frac{2}{3}}) - lo g_{10} (y^{2})

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

= - (lo g_{10} (x^{\frac{2}{3}}) + lo g_{10} (y^{2}))

Apply log rule:

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

lo g_{10} (x^{\frac{2}{3}}) + lo g_{10} (y^{2}) = lo g_{10} (y^{2} x^{\frac{2}{3}})

= - lo g_{10} (x^{\frac{2}{3}} y^{2})

1 + \frac{1}{2} lo g_{10} (p + 4) - lo g_{10} (x)

7 ln (x + 9) - 8 ln (x)

ln (\frac{y}{x} - 4) + 6 (\frac{1}{5} ln (\frac{y}{x} - 1) - \frac{1}{5} ln (\frac{y}{x} + 4)) + ln (x)

\frac{3}{8} \cdot ln (\frac{8}{3}) + (\frac{5}{16} \cdot ln (\frac{16}{5})) \cdot 2

ln (\frac{1}{d}) - ln (\frac{1}{y})

What is simplify-2/3 log_{10}(x)-2log_{10}(y) ?
The solution to simplify-2/3 log_{10}(x)-2log_{10}(y) is -log_{10}(x^{2/3}y^2)