What is log_{10}((sqrt(x))/(y^5z^9)) ?

The solution to log_{10}((sqrt(x))/(y^5z^9)) is log_{10}(sqrt(x))-5log_{10}(y)-9log_{10}(z)

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simplify log_{10}((sqrt(x))/(y^5z^9))

simplify

lo g_{10} (\frac{x}{y ^{5} z ^{9}})

lo g_{10} (x) - 5 lo g_{10} (y) - 9 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x}{y ^{5} z ^{9}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{x}{y ^{5} z ^{9}}) = lo g_{10} (x) - lo g_{10} (y^{5} z^{9})

= lo g_{10} (x) - lo g_{10} (y^{5} z^{9})

Simplify

lo g_{10} (y^{5} z^{9}) : 5 lo g_{10} (y) + 9 lo g_{10} (z)

= lo g_{10} (x) - (5 lo g_{10} (y) + 9 lo g_{10} (z))

Apply the distributive law:

- (a + b) = - a - b

- (5 lo g_{10} (y) + 9 lo g_{10} (z)) = - 5 lo g_{10} (y) - 9 lo g_{10} (z)

= lo g_{10} (x) - 5 lo g_{10} (y) - 9 lo g_{10} (z)

lo g_{10} (\frac{x ^{2} + y ^{2}}{1000000})

lo g_{7} (\frac{343 b ^{7} y ^{2} - 4}{y ( x + 4 ) ^{2}})

2 lo g_{e} (4) + 2 lo g_{e} (5)

10 lo g_{10} (x) + \frac{2}{3} lo g_{10} (64)

ln (15 x)

What is log_{10}((sqrt(x))/(y^5z^9)) ?
The solution to log_{10}((sqrt(x))/(y^5z^9)) is log_{10}(sqrt(x))-5log_{10}(y)-9log_{10}(z)