What is log_{10}((a^5b^7)/(c^2)) ?

The solution to log_{10}((a^5b^7)/(c^2)) is 5log_{10}(a)+7log_{10}(b)-2log_{10}(c)

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simplify log_{10}((a^5b^7)/(c^2))

simplify

lo g_{10} (\frac{a ^{5} b ^{7}}{c ^{2}})

5 lo g_{10} (a) + 7 lo g_{10} (b) - 2 lo g_{10} (c)

Solution steps

lo g_{10} (\frac{a ^{5} b ^{7}}{c ^{2}})

Apply log rule:

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

lo g_{10} (\frac{a ^{5} b ^{7}}{c ^{2}}) = lo g_{10} (a^{5} b^{7}) - lo g_{10} (c^{2})

= lo g_{10} (a^{5} b^{7}) - lo g_{10} (c^{2})

lo g_{10} (a^{5} b^{7}) = 5 lo g_{10} (a) + 7 lo g_{10} (b)

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

= 5 lo g_{10} (a) + 7 lo g_{10} (b) - 2 lo g_{10} (c)

ln (x^{5} - 1) - ln (x^{3} - 1)

3 lo g_{10} (x + 1) + lo g_{10} (y) - 2 lo g_{10} (x)

2 lo g_{10} (x) - lo g_{10} (\frac{1}{x}) - lo g_{10} (y)

lo g_{10} (\frac{2 x ^{3} + 4}{5 x ^{3} - x})

33.33 (1) ln (\frac{1100}{1400}) - 0.287 ln (\frac{5}{20})

What is log_{10}((a^5b^7)/(c^2)) ?
The solution to log_{10}((a^5b^7)/(c^2)) is 5log_{10}(a)+7log_{10}(b)-2log_{10}(c)