What is log_{10}(4x)-log_{10}(12+sqrt(x)) ?

The solution to log_{10}(4x)-log_{10}(12+sqrt(x)) is log_{10}((4x)/(12+sqrt(x)))

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simplify log_{10}(4x)-log_{10}(12+sqrt(x))

simplify

lo g_{10} (4 x) - lo g_{10} (12 + x)

lo g_{10} (\frac{4 x}{12 + x})

Solution steps

lo g_{10} (4 x) - lo g_{10} (12 + x)

Simplify

lo g_{10} (4 x) : 2 lo g_{10} (2) + lo g_{10} (x)

= (2 lo g_{10} (2) + lo g_{10} (x)) - lo g_{10} (12 + x)

Apply rule:

(a) = a

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

= 2 lo g_{10} (2) + lo g_{10} (x) - lo g_{10} (12 + x)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

= lo g_{10} (2^{2}) + lo g_{10} (x) - lo g_{10} (12 + x)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

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

= lo g_{10} (2^{2} x) - lo g_{10} (12 + x)

Apply log rule:

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

lo g_{10} (2^{2} x) - lo g_{10} (12 + x) = lo g_{10} (\frac{2 ^{2} x}{12 + x})

= lo g_{10} (\frac{2 ^{2} x}{12 + x})

Simplify

\frac{2 ^{2} x}{12 + x} : \frac{4 x}{12 + x}

= lo g_{10} (\frac{4 x}{12 + x})

ln (\frac{x ^{2} - 7}{( x - 3 ) ^{4}})

ln (2 x - 1) - ln (x + 4)

lo g_{10} (4^{- 1}) + lo g_{10} (\frac{1}{2})

lo g_{10} (\frac{3 a ^{3}}{5 b})

ln (a e^{- a x})

What is log_{10}(4x)-log_{10}(12+sqrt(x)) ?
The solution to log_{10}(4x)-log_{10}(12+sqrt(x)) is log_{10}((4x)/(12+sqrt(x)))