What is log_{10}((x^2)/(10(x+20))) ?

The solution to log_{10}((x^2)/(10(x+20))) is 2log_{10}(x)-1-log_{10}(x+20)

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simplify log_{10}((x^2)/(10(x+20)))

simplify

lo g_{10} (\frac{x ^{2}}{10 ( x + 20 )})

2 lo g_{10} (x) - 1 - lo g_{10} (x + 20)

Solution steps

lo g_{10} (\frac{x ^{2}}{10 ( x + 20 )})

Apply log rule:

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

lo g_{10} (\frac{x ^{2}}{10 ( x + 20 )}) = lo g_{10} (x^{2}) - lo g_{10} (10 (x + 20))

= lo g_{10} (x^{2}) - lo g_{10} (10 (x + 20))

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

lo g_{10} (10 (x + 20)) = 1 + lo g_{10} (x + 20)

= 2 lo g_{10} (x) - (1 + lo g_{10} (x + 20))

Apply the distributive law:

- (a + b) = - a - b

- (1 + lo g_{10} (x + 20)) = - 1 - lo g_{10} (x + 20)

= 2 lo g_{10} (x) - 1 - lo g_{10} (x + 20)

lo g_{b} (\frac{x y ^{3}}{z ^{6}})

lo g_{4} ((\frac{2 p}{q ^{5}})^{3})

lo g_{5} (\frac{25}{x + 6})

ln (y) + ln (x + 1)

lo g_{81} (\frac{( x - 5 )}{3 ( x + 4 ) ^{5}})

What is log_{10}((x^2)/(10(x+20))) ?
The solution to log_{10}((x^2)/(10(x+20))) is 2log_{10}(x)-1-log_{10}(x+20)