What is log_{10}((a^2)/(2a^{1/2)}) ?

The solution to log_{10}((a^2)/(2a^{1/2)}) is 3/2 log_{10}(a)-log_{10}(2)

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simplify log_{10}((a^2)/(2a^{1/2)})

simplify

lo g_{10} (\frac{a ^{2}}{2 a ^{\frac{1}{2}}})

\frac{3}{2} lo g_{10} (a) - lo g_{10} (2)

Solution steps

lo g_{10} (\frac{a ^{2}}{2 a ^{\frac{1}{2}}})

Simplify

\frac{a ^{2}}{a ^{\frac{1}{2}}} : a^{\frac{3}{2}}

= lo g_{10} (\frac{a ^{\frac{3}{2}}}{2})

Apply log rule:

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

lo g_{10} (\frac{a ^{\frac{3}{2}}}{2}) = lo g_{10} (a^{\frac{3}{2}}) - lo g_{10} (2)

= lo g_{10} (a^{\frac{3}{2}}) - lo g_{10} (2)

Simplify

lo g_{10} (a^{\frac{3}{2}}) : \frac{3}{2} lo g_{10} (a)

= \frac{3}{2} lo g_{10} (a) - lo g_{10} (2)

(2 x + 7) (x - 3)

\frac{2 ^{3}}{3 !}

(y + 3) (y + 5)

4 x (- 5 x^{2} + 3 x - 2) + (x^{2} - 3 x + 1) (x^{2} - 3)

- 11 \times 1

What is log_{10}((a^2)/(2a^{1/2)}) ?
The solution to log_{10}((a^2)/(2a^{1/2)}) is 3/2 log_{10}(a)-log_{10}(2)