What is 5log_{10}(x)+4log_{10}(y) ?

The solution to 5log_{10}(x)+4log_{10}(y) is log_{10}(x^5y^4)

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simplify 5log_{10}(x)+4log_{10}(y)

simplify

5 lo g_{10} (x) + 4 lo g_{10} (y)

lo g_{10} (x^{5} y^{4})

Solution steps

5 lo g_{10} (x) + 4 lo g_{10} (y)

Apply log rule:

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

5 lo g_{10} (x) = lo g_{10} (x^{5})

= lo g_{10} (x^{5}) + 4 lo g_{10} (y)

Apply log rule:

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

4 lo g_{10} (y) = lo g_{10} (y^{4})

= lo g_{10} (x^{5}) + lo g_{10} (y^{4})

Apply log rule:

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

lo g_{10} (x^{5}) + lo g_{10} (y^{4}) = lo g_{10} (x^{5} y^{4})

= lo g_{10} (x^{5} y^{4})

\frac{1}{3} ln (6 + 35)

\frac{1}{2} ln ∣ (8.7) + 4 ∣ - \frac{1}{2} ln ∣ (8.7) + 6 ∣ + C

ln (\frac{27}{2}) - 1

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

What is 5log_{10}(x)+4log_{10}(y) ?
The solution to 5log_{10}(x)+4log_{10}(y) is log_{10}(x^5y^4)