What is log_{10}((9x^5)/(y^6)) ?

The solution to log_{10}((9x^5)/(y^6)) is 2log_{10}(3)+5log_{10}(x)-6log_{10}(y)

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simplify log_{10}((9x^5)/(y^6))

simplify

lo g_{10} (\frac{9 x ^{5}}{y ^{6}})

2 lo g_{10} (3) + 5 lo g_{10} (x) - 6 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{9 x ^{5}}{y ^{6}})

Apply log rule:

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

lo g_{10} (\frac{9 x ^{5}}{y ^{6}}) = lo g_{10} (9 x^{5}) - lo g_{10} (y^{6})

= lo g_{10} (9 x^{5}) - lo g_{10} (y^{6})

lo g_{10} (9 x^{5}) = 2 lo g_{10} (3) + 5 lo g_{10} (x)

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

= 2 lo g_{10} (3) + 5 lo g_{10} (x) - 6 lo g_{10} (y)

lo g_{10} (6) - 2 lo g_{10} (y)

lo g_{b} (\frac{x ^{2}}{y z ^{2}})

lo g_{b} (6) - lo g_{b} (3)

lo g_{7} (3 x) - lo g_{7} (9 x) + lo g_{7} (6 y)

3 [lo g_{10} (a) + lo g_{10} (a + 1)] - lo g_{10} (b)

What is log_{10}((9x^5)/(y^6)) ?
The solution to log_{10}((9x^5)/(y^6)) is 2log_{10}(3)+5log_{10}(x)-6log_{10}(y)