What is 1/2 log_{10}(x)+6log_{10}(y) ?

The solution to 1/2 log_{10}(x)+6log_{10}(y) is log_{10}(x^{1/2}y^6)

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simplify 1/2 log_{10}(x)+6log_{10}(y)

simplify

\frac{1}{2} lo g_{10} (x) + 6 lo g_{10} (y)

lo g_{10} (x^{\frac{1}{2}} y^{6})

Solution steps

\frac{1}{2} lo g_{10} (x) + 6 lo g_{10} (y)

Apply log rule:

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

\frac{1}{2} lo g_{10} (x) = lo g_{10} (x^{\frac{1}{2}})

= lo g_{10} (x^{\frac{1}{2}}) + 6 lo g_{10} (y)

Apply log rule:

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

6 lo g_{10} (y) = lo g_{10} (y^{6})

= lo g_{10} (x^{\frac{1}{2}}) + lo g_{10} (y^{6})

Apply log rule:

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

lo g_{10} (x^{\frac{1}{2}}) + lo g_{10} (y^{6}) = lo g_{10} (y^{6} x^{\frac{1}{2}})

= lo g_{10} (x^{\frac{1}{2}} y^{6})

\frac{1}{3} (ln (\frac{x}{3} + 1) - ln (\frac{x}{3} - 1))

- (\frac{3}{14}) lo g_{2} (\frac{3}{14}) - (\frac{2}{14}) lo g_{2} (\frac{2}{14})

ln (\frac{28500}{19250})

3 lo g_{2} (5) - lo g_{2} (3) + lo g_{2} (6)

\frac{1}{3} (6 ln (x + 4) + ln (x) - ln (x^{2} - 8))

What is 1/2 log_{10}(x)+6log_{10}(y) ?
The solution to 1/2 log_{10}(x)+6log_{10}(y) is log_{10}(x^{1/2}y^6)