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

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

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

simplify

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

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

Solution steps

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

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

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

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

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

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

Apply log rule:

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

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

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

\frac{1}{3} lo g_{10} (27) - \frac{1}{2} lo g_{10} (49)

ln ((2) e^{7 b})

\frac{( \frac{- 6 l n ^{3} ( 2 ) + 13 l n ^{2} ( 2 ) + 18 l n ( x ) + 12}{16 l n ^{5} ( 2 )} )}{120}

lo g_{10} (310 z)

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