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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

lo g_{10} (b^{4} c) = 4 lo g_{10} (b) + lo g_{10} (c)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

lo g_{3} (5) + 5 lo g_{3} (2)

lo g_{4} (3) + lo g_{4} (5)

lo g_{3} (x y)

lo g_{7} (3 x)

ln (\frac{x}{x - 6}) + ln (\frac{x + 6}{x}) - ln (x^{2} - 36)

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