What is 7log_{10}(z)+5log_{10}(x)+3log_{10}(y) ?

The solution to 7log_{10}(z)+5log_{10}(x)+3log_{10}(y) is log_{10}(z^7x^5y^3)

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simplify 7log_{10}(z)+5log_{10}(x)+3log_{10}(y)

simplify

7 lo g_{10} (z) + 5 lo g_{10} (x) + 3 lo g_{10} (y)

lo g_{10} (z^{7} x^{5} y^{3})

Solution steps

7 lo g_{10} (z) + 5 lo g_{10} (x) + 3 lo g_{10} (y)

Apply log rule:

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

7 lo g_{10} (z) = lo g_{10} (z^{7})

= lo g_{10} (z^{7}) + 5 lo g_{10} (x) + 3 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} (z^{7}) + lo g_{10} (x^{5}) + 3 lo g_{10} (y)

Apply log rule:

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

lo g_{10} (z^{7}) + lo g_{10} (x^{5}) = lo g_{10} (z^{7} x^{5})

= lo g_{10} (z^{7} x^{5}) + 3 lo g_{10} (y)

Apply log rule:

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

3 lo g_{10} (y) = lo g_{10} (y^{3})

= lo g_{10} (z^{7} x^{5}) + lo g_{10} (y^{3})

Apply log rule:

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

lo g_{10} (z^{7} x^{5}) + lo g_{10} (y^{3}) = lo g_{10} (z^{7} x^{5} y^{3})

= lo g_{10} (z^{7} x^{5} y^{3})

lo g_{b} (\frac{0.34}{0.83})

ln^{2} (a + a^{2} + x^{2}) - ln^{2} (x)

\frac{1}{3} (ln (15) - ln (6))

\frac{8 ^{x + 1}}{3 ln ( 2 )} + C

6.1 + lo g_{10} (\frac{15}{0.03 \cdot 51})

What is 7log_{10}(z)+5log_{10}(x)+3log_{10}(y) ?
The solution to 7log_{10}(z)+5log_{10}(x)+3log_{10}(y) is log_{10}(z^7x^5y^3)