What is log_{10}((sqrt(x))/(100y^7)) ?

The solution to log_{10}((sqrt(x))/(100y^7)) is log_{10}(sqrt(x))-2-7log_{10}(y)

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simplify log_{10}((sqrt(x))/(100y^7))

simplify

lo g_{10} (\frac{x}{100 y ^{7}})

lo g_{10} (x) - 2 - 7 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{100 y ^{7}})

Apply log rule:

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

lo g_{10} (\frac{x}{100 y ^{7}}) = lo g_{10} (x) - lo g_{10} (100 y^{7})

= lo g_{10} (x) - lo g_{10} (100 y^{7})

Simplify

lo g_{10} (100 y^{7}) : 2 + 7 lo g_{10} (y)

= lo g_{10} (x) - (2 + 7 lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (2 + 7 lo g_{10} (y)) = - 2 - 7 lo g_{10} (y)

= lo g_{10} (x) - 2 - 7 lo g_{10} (y)

ln (x^{5} 3 - x)

ln (\frac{x ^{4}}{x ( 1 + x ) ^{3}})

lo g_{5} (4) - lo g_{5} (11)

lo g_{\frac{1}{3}} (2 x)

2 lo g_{c} (x) + 5 lo g_{c} (y) - 5 lo g_{c} (x)

What is log_{10}((sqrt(x))/(100y^7)) ?
The solution to log_{10}((sqrt(x))/(100y^7)) is log_{10}(sqrt(x))-2-7log_{10}(y)