What is log_{10}((pir^3h)/3) ?

The solution to log_{10}((pir^3h)/3) is log_{10}(pi)+3log_{10}(r)+log_{10}(h)-log_{10}(3)

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simplify log_{10}((pir^3h)/3)

simplify

lo g_{10} (\frac{π r ^{3} h}{3})

lo g_{10} (π) + 3 lo g_{10} (r) + lo g_{10} (h) - lo g_{10} (3)

Solution steps

lo g_{10} (\frac{π r ^{3} h}{3})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{π r ^{3} h}{3}) = lo g_{10} (π r^{3} h) - lo g_{10} (3)

= lo g_{10} (πh r^{3}) - lo g_{10} (3)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (π r^{3} h) = lo g_{10} (π) + lo g_{10} (r^{3}) + lo g_{10} (h)

= lo g_{10} (π) + lo g_{10} (r^{3}) + lo g_{10} (h) - lo g_{10} (3)

Apply log rule:

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

lo g_{10} (r^{3}) = 3 lo g_{10} (r)

= lo g_{10} (π) + 3 lo g_{10} (r) + lo g_{10} (h) - lo g_{10} (3)

ln (2 \cdot x_{1} x_{2} x_{3})

- 3 ln (x) - 2 ln (y)

2 ln (3 x - 8) - ln (5 x + 1)

ln (1) + ln (\frac{1}{2})

\frac{1}{9} ln (\frac{1}{8})

What is log_{10}((pir^3h)/3) ?
The solution to log_{10}((pir^3h)/3) is log_{10}(pi)+3log_{10}(r)+log_{10}(h)-log_{10}(3)