What is expand log_{10}((24m^2)/(16p)) ?

The solution to expand log_{10}((24m^2)/(16p)) is log_{10}(24)+2log_{10}(m)-4log_{10}(2)-log_{10}(p)

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expand log_{10}((24m^2)/(16p))

expand

lo g_{10} (\frac{24 m ^{2}}{16 p})

lo g_{10} (24) + 2 lo g_{10} (m) - 4 lo g_{10} (2) - lo g_{10} (p)

Solution steps

lo g_{10} (\frac{24 m ^{2}}{16 p})

Apply log rule:

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

lo g_{10} (\frac{24 m ^{2}}{16 p}) = lo g_{10} (24 m^{2}) - lo g_{10} (16 p)

= lo g_{10} (24 m^{2}) - lo g_{10} (16 p)

Apply log rule:

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

lo g_{10} (24 m^{2}) = lo g_{10} (24) + lo g_{10} (m^{2}), lo g_{10} (16 p) = lo g_{10} (16) + lo g_{10} (p)

= lo g_{10} (24) + lo g_{10} (m^{2}) - (lo g_{10} (p) + lo g_{10} (16))

Apply log rule:

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

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

= lo g_{10} (24) + 2 lo g_{10} (m) - (lo g_{10} (16) + lo g_{10} (p))

lo g_{10} (16) = 4 lo g_{10} (2)

= lo g_{10} (24) + 2 lo g_{10} (m) - (lo g_{10} (p) + 4 lo g_{10} (2))

- (4 lo g_{10} (2) + lo g_{10} (p)) : - 4 lo g_{10} (2) - lo g_{10} (p)

= lo g_{10} (24) + 2 lo g_{10} (m) - 4 lo g_{10} (2) - lo g_{10} (p)

ln (e^{x} \frac{x}{4 x})

ln (ln (a + b) + ln (a - b) - 8 ln (c))

- \frac{1}{5} lo g_{3} (2)

ln (\frac{x - 2}{x + 2})

lo g_{2} (2 x) - 2 lo g_{2} (y) + lo g_{2} (z)

What is expand log_{10}((24m^2)/(16p)) ?
The solution to expand log_{10}((24m^2)/(16p)) is log_{10}(24)+2log_{10}(m)-4log_{10}(2)-log_{10}(p)