What is log_{5}((a^2b^2x)/(c^3)) ?

The solution to log_{5}((a^2b^2x)/(c^3)) is 2log_{5}(a)+2log_{5}(b)+log_{5}(x)-3log_{5}(c)

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simplify log_{5}((a^2b^2x)/(c^3))

simplify

lo g_{5} (\frac{a ^{2} b ^{2} x}{c ^{3}})

2 lo g_{5} (a) + 2 lo g_{5} (b) + lo g_{5} (x) - 3 lo g_{5} (c)

Solution steps

lo g_{5} (\frac{a ^{2} b ^{2} x}{c ^{3}})

Apply log rule:

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

lo g_{5} (\frac{a ^{2} b ^{2} x}{c ^{3}}) = lo g_{5} (a^{2} b^{2} x) - lo g_{5} (c^{3})

= lo g_{5} (a^{2} b^{2} x) - lo g_{5} (c^{3})

lo g_{5} (a^{2} b^{2} x) = 2 lo g_{5} (a) + 2 lo g_{5} (b) + lo g_{5} (x)

lo g_{5} (c^{3}) = 3 lo g_{5} (c)

= 2 lo g_{5} (a) + 2 lo g_{5} (b) + lo g_{5} (x) - 3 lo g_{5} (c)

lo g_{10} (\frac{x y ^{2}}{z})

ln (y e^{x})

- lo g_{10} (4.5 \cdot 1 0^{- 4})

ln (\frac{x ^{2}}{x ( 1 + x ) ^{5}})

lo g_{2} (8 x y)

What is log_{5}((a^2b^2x)/(c^3)) ?
The solution to log_{5}((a^2b^2x)/(c^3)) is 2log_{5}(a)+2log_{5}(b)+log_{5}(x)-3log_{5}(c)