What is log_{10}(a)+4log_{10}(b)-2log_{10}(c) ?

The solution to log_{10}(a)+4log_{10}(b)-2log_{10}(c) is log_{10}((ab^4)/(c^2))

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simplify log_{10}(a)+4log_{10}(b)-2log_{10}(c)

simplify

lo g_{10} (a) + 4 lo g_{10} (b) - 2 lo g_{10} (c)

lo g_{10} (\frac{a b ^{4}}{c ^{2}})

Solution steps

lo g_{10} (a) + 4 lo g_{10} (b) - 2 lo g_{10} (c)

Apply log rule:

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

4 lo g_{10} (b) = lo g_{10} (b^{4})

= lo g_{10} (a) + lo g_{10} (b^{4}) - 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^{4}) = lo g_{10} (a b^{4})

= lo g_{10} (a b^{4}) - 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^{4}) - 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^{4}) - lo g_{10} (c^{2}) = lo g_{10} (\frac{a b ^{4}}{c ^{2}})

= lo g_{10} (\frac{a b ^{4}}{c ^{2}})

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

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

lo g_{2} (\frac{x}{y})

ln (\frac{x ^{6}}{x ^{2} - 25})

ln (e^{- θ n} (θ))

What is log_{10}(a)+4log_{10}(b)-2log_{10}(c) ?
The solution to log_{10}(a)+4log_{10}(b)-2log_{10}(c) is log_{10}((ab^4)/(c^2))