What is log_{10}((a^4)/(b^2c^3)) ?

The solution to log_{10}((a^4)/(b^2c^3)) is 4log_{10}(a)-2log_{10}(b)-3log_{10}(c)

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simplify log_{10}((a^4)/(b^2c^3))

simplify

lo g_{10} (\frac{a ^{4}}{b ^{2} c ^{3}})

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

Solution steps

lo g_{10} (\frac{a ^{4}}{b ^{2} c ^{3}})

Apply log rule:

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

lo g_{10} (\frac{a ^{4}}{b ^{2} c ^{3}}) = lo g_{10} (a^{4}) - lo g_{10} (b^{2} c^{3})

= lo g_{10} (a^{4}) - lo g_{10} (b^{2} c^{3})

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

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

= 4 lo g_{10} (a) - (2 lo g_{10} (b) + 3 lo g_{10} (c))

Apply the distributive law:

- (a + b) = - a - b

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

= 4 lo g_{10} (a) - 2 lo g_{10} (b) - 3 lo g_{10} (c)

lo g_{9} (\frac{y}{81})

lo g_{7} (\frac{g}{49})

(\frac{2}{3}) lo g_{10} (\frac{E}{0.7})

ln (5) + ln (x) + ln (y)

ln (8) - ln (3)

What is log_{10}((a^4)/(b^2c^3)) ?
The solution to log_{10}((a^4)/(b^2c^3)) is 4log_{10}(a)-2log_{10}(b)-3log_{10}(c)