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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln ((\frac{1}{x})^{\frac{1}{l n ( x )}})

ln (\frac{486}{271})

\frac{4 ln ( 2 )}{ln ( \frac{512}{3} )}

ln (\frac{400}{100})

ln (\frac{4421}{28350})

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