What is log_{10}(a)+3log_{10}(b)-2log_{10}(c) ?

The solution to log_{10}(a)+3log_{10}(b)-2log_{10}(c) is log_{10}((ab^3)/(c^2))

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simplify log_{10}(a)+3log_{10}(b)-2log_{10}(c)

simplify

lo g_{10} (a) + 3 lo g_{10} (b) - 2 lo g_{10} (c)

lo g_{10} (\frac{a b ^{3}}{c ^{2}})

Solution steps

lo g_{10} (a) + 3 lo g_{10} (b) - 2 lo g_{10} (c)

Apply log rule:

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

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

= lo g_{10} (a) + lo g_{10} (b^{3}) - 2 lo g_{10} (c)

Apply log rule:

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

lo g_{10} (a) + lo g_{10} (b^{3}) = lo g_{10} (a b^{3})

= lo g_{10} (a b^{3}) - 2 lo g_{10} (c)

Apply log rule:

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

2 lo g_{10} (c) = lo g_{10} (c^{2})

= lo g_{10} (a b^{3}) - lo g_{10} (c^{2})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (a b^{3}) - lo g_{10} (c^{2}) = lo g_{10} (\frac{a b ^{3}}{c ^{2}})

= lo g_{10} (\frac{a b ^{3}}{c ^{2}})

lo g_{d} (u^{3} v^{4})

lo g_{6} (x^{2}) - lo g_{6} (x) - lo g_{6} (y)

lo g_{10} (8) - 2 lo g_{10} (6) - lo g_{10} (3)

ln (\frac{4}{4 + 2})

lo g_{8} (\frac{z}{64})

What is log_{10}(a)+3log_{10}(b)-2log_{10}(c) ?
The solution to log_{10}(a)+3log_{10}(b)-2log_{10}(c) is log_{10}((ab^3)/(c^2))